University  of  California  •  Berkeley 

The  Theodore  P.  Hill  Collection 

of 
Early  American  Mathematics  Books 


1 


THE 


PEIMAEY 

ARITHMETIC. 


DESIGNED   AS 


A.N"  INTEODUCTION  TO  MENTAL  AND  WRITTEN 
ARITHMETIC. 


BY 

PHILOTUS  DEAK  A.M. 


PITTSBURGH: 
PUBLISHED  BY  A.  II.  ENGLISH  &  CO. 

98  FOURTH  STREET. 


-« 


Entered  according  to  Act  of  Congress,  in  the  year  1860,  by 

A.  H.  ENGLISH  &  CO., 

in  the  Clerk's  Office  of  the  District  Court  of  the  United  States  for  the 
Western  District  of  Pennsylvania. 


STEREOTYPED    BY  L.  JOHNSON  AND  CO. 
PHILADELPHIA. 


CAXTON  PRESS  OF 
SHERMAN  &  CO.,  PHILADELPHIA. 


9 


PREFACE. 


This  work  is  designed  for  those  who  are  acquiring  their 
first  ideas  of  the  science  of  Arithmetic.  In  its  stjde  and 
material,  it  is  strictly  elementary,  and  thus  adapted  to  the 
capacities  of  children  beginning  the  study  of  numbers.  In 
its  arrangement,  it  is  strictly  progressive.  Commencing 
with  the  idea  of  natural  unity,  it  first  aims  to  represent  to 
the  eye  the  smallest  assemblages  of  those  units,  to  give 
just  conceptions  of  such  numbers  as  a  whole,  while  teach- 
ing the  art  of  counting,  by  which  we  gain  a  knowledge  of 
those  numbers.  After  explaining  the  symbols  of  number, 
called  figures^  it  takes  the  pupil,  by  easy  steps,  through  the 
tables  and  exercises  of  the  four  fundamental  rules.  Then 
follow  corresponding  explanations  and  exercises  in  the 
same  part  of  Written  Arithmetic,  in  which  he  is  taught  to 
read,  write,  add,  subtract,  multiply,  and  divide  with  simple 
numbers,  of  sufficient  magnitude  to  give  him  knowledge 
and  skill  in  small  operations.  Next  come  Fractions,  only 
developed  enough  to  give  the  pupil  their  elementary  ideas, 
and  familiarity  with  their  simple  processes.  Finally,  he  is 
taught  and  exercised  upon  the  usual  statistical  tables,  to 
give  him  information  upon  the  common  matters  of  money, 
weight,  and  measure. 

It  is  believed  that  the  scope  of  this  book  is  sufficient  to 
prepare  the  pupil  for  easy  and  rapid  advancement  through 
Mental  and  Written  Arithmetic,  which  should  follow  the 
study  of  this,  in  the  order  in  which  they  are  named. 

If  the  cause  of  Public  Education  is  promoted  by  this 
little  work,  it  will  fulfill  the  design  of  its  composition,  and 
gratify  the  highest  wishes  of  The  Author. 


SUGGESTIONS  TO  TEACHERS. 


1.  It  should  always  be  borne  in  mind  that  this  is  the 
child's  first  book  of  Arithmetic,  and  that  the  work  of 
education,  if  well  done  now,  will  have  its  greatest  ef- 
ficiency. 

2.  Aim  always  to  secure  the  pupil's  clear  comprehension 
of  every  point  as  he  advances.  Do  not  think  repetition 
useless,  till  his  answers  are  perfectly  prompt  and  clear. 

3.  Drill  the  memory  on  the  sections  of  the  tables,  in 
every  possible  order  of  saying  them,  till  every  statement 
in  them  is  at  perfect  and  instantaneous  command. 

4.  Assign  every  task  a  sufficiently  long  time  before  reci- 
tation to  have  it  thoroughly  acquired. 

5.  Do  not  allow  the  pupils  to  use  the  book  in  recitation. 

6.  Use  the  blackboard  often  for  explanation,  as  well  as 
for  the  written  processes  of  the  lessons. 

7.  Manage  the  recitations  of  large  classes  so  that  every 
pupil  in  the  class  may  have  his  interest  excited  in  every 
question  and  process. 

8.  Kequire  a  full  analysis  with  the  answer  to  every 
question,  generally  following  some  definite  form  of  words. 

9.  After  the  mental  solution  of  a  question,  require  the 
pupil  to  perform  the  written  process,  and  explain  it. 


-a 


PRIMARY   ARITHMETIC. 


LESSON    I. 

One  tree  and         one  tree         are  two  trees. 


Two  trees         and       one  tree       are        three  trees. 


Three  houses     and     one  house     are     four  houses. 


Six  balls 


and 

and 
and 


one  man 


five  men. 


one  ball 
one  ball 


are 


are         six  balls. 
are       seven  balls. 


Seven  marks     and  one  mark     are      eight  marks. 

I  I  I  I  I  I  I  I  I  I  I  I  I  I  I  I 

Eight  cents       and  one  cent        are         nine  cents. 

oooooooo       o     ooooooooo 


1* 


COUNTING. 


Nine  cents         and        one  cent  are         ten  cents. 

OOOOOOOOO      O     OOOOOOOOOO 
When  we  count  things,  we  notice  them  one  by  one, 
and  think  how  many  each  one  makes  with  those  noticed 
before  it.     In  counting  ten  things  we  say, 
one   two   three    four    five    six    seven    eight    nine   ten. 


Note  to  Teachers. — Let  the  pupil  be  now  exercised  by 
counting  ten  visible  things,  such  as  marks  on  the  blackboard, 
books,  schoolmates,  panes  of  glass  in  the  window,  &c.,  till  he  is 
perfect  in  the  exercise 


LESSON    II. 

Ten  and  one  are  eleven ;  one  more  makes  twelve ;  one 
more  thirteen;  one  more  fourteen ;  one  more  fifteen;  one 
more  sixteen;  one  more  seventeen;  one  more  eighteen; 
one  more  nineteen;  and  one  more  makes  twenty. 

Now  count  this  row  of  balls. 

One,  two,  &c. 

Note. — Let  the  pupil  be  exercised  in  counting  twenty  things, 
of  various  kinds,  till  perfect  in  his  knowledge  as  far  as  twenty. 

Twenty  and  one  are  twenty -one ;  one  more  makes 
twenty 'two ;  one  more  twenty-three;  one  more  twenty- 
four;  one  more  twenty-five;  one  more  tioenty-six  ;  one 
more  twenty-seven;  one  more  tw enty -eight ;  one  more 
twenty-nine  ;  and  one  more  makes  thirty. 

Now  count  the  balls  in  the  row  above,  and  then  keep 
on  in  th^-S  row. 

Twenty-one,  &c. 

From  this  we  see  that  the  word  twenty^  with  the  name 
of  a  number  less  than  ten,  makes  the  name  of  a  number 
between  twenty  and  thirty. 


& 

COUNTING. 


LESSON    III. 

Count  the  balls  in  these  rows,  making  the  names  of 
numbers  as  you  did  from  twenty  to  thirty. 

Thirty,  thirty-one 
Forty,  forty-one 


Fifty,  fifty-one 

Sixty 

Seventy 


Eighty 
Ninety 
One  hundred. 


If  you  count  in  this  way  as  far  as  one  hundred  and 
ninety-nine,  the  next  one  makes  two  hundred. 

After  two  hundred  and  ninety -nine  comes  three  hun- 
dred ;  after  three  hundred  and  ninety-nine  comes  /our 
hundred  ;  and  so  on  till  you  come  to  nine  hundred  and 
ninety-nine,  when  the  next  one  makes  one  thousand, 
which  is  the  same  as  ten  hundred. 

Note  to  Teacheks. — Now  let  the  pupil  be  exercised  upon  the 
sections  of  this  lesson,  one  by  one,  and  compare  them. 


NOTATION. 


LESSON    IV. 

When  we  write  numbers,  it  is  too  much  trouble  to 
write  them  out  in  words.  We  make  marks  which  have 
the  same  meaning  as  the  words.  These  marks  are  called 
figures. 


NUMBERS 

ARABIC 

Printed. 

FIGURES. 

Written, 

ROMAN. 

Naught,  nothing,  or  cipher      0 
One          ....     1 

0 

4 

I. 

Two 

-     2 

2 

II. 

Three       - 

-    3 

3 

Ill 

Four 

-    4 

A 

IV. 

Five 

.    6 

5 

V. 

Six 

-    6 

6 

YI. 

Seven 

.    7 

7 

YII. 

Eight 
Nine 

-  8 

-  9 

9 

VIII. 
IX. 

Ten 

.  10 

40 

X. 

Eleven     - 

-  11 

44 

XI. 

Twelve     - 

.  12 

42 

XII. 

Thirteen 

-  13 

43 

XIII. 

Fourteen 

-  14 

4j^ 

XTV. 

Fifteen     - 

-  15 

45 

XV. 

Sixteen 

.  16 

46 

XVI. 

Seventeen 

-  17 

47 

XVII. 

Eighteen 

.  18 

4^ 

XVIII. 

Nineteen 

-  19 

49 

XIX. 

Twenty    -         -         -         -  20             SO              XX. 

What    figures    has    twelve  ?      Sixteen  */      Fourteen  ? 
Seventeen?    Twenty?    Thirteen?    Eighteen?    Nineteen? 

The  Roman  figures  are  only  used  for  heads  of  chap- 
ters, for  the  faces  of  clocks,  &c. 

R ■ 

NOTATION. 

9 

LESSON 

V. 

Twenty-one  - 

21 

S4 

XXI. 

Twenty-two  - 

22 

22 

XXII. 

Twenty-three 

23 

23 

XXIII. 

Twenty-four 

24 

Si 

XXIV. 

Twenty-five  - 

25 

25 

XXV. 

Twenty-six    - 

26 

26 

XXVI. 

Twenty-seven 

27 

27 

XXVII. 

Twenty-eight 

28 

2^ 

XXVIII. 

Twenty-nine 

29 

29 

XXIX. 

Thirty 

30 

30 

XXX. 

Forty 

40 

iO 

XL. 

Fifty 

50 

50 

L. 

Sixty 

60 

60 

LX. 

Seventy 

70 

70 

LXX. 

Eighty 

80 

^0 

LXXX. 

Ninety 

90 

90 

xc. 

One  hundred 

100 

400 

c. 

Two  hundred 

200 

200 

cc. 

Two  hundred  an 

d  six     - 

206 

206 

CCVI. 

Three  hundred 

. 

300 

300 

ccc. 

Four  hundred 

. 

400 

MO 

CCCCorCD. 

Five  hundred 

• 

500 

500 

D. 

Six  hundred 

. 

600 

600 

DC. 

Six  hundred  and  twelve 

612 

642 

DCXII. 

Seven  hundred 

- 

- 

700 

700 

DCC. 

Eight  hundred 

- 

. 

800 

ioo 

DCCC. 

Nine  hundred 

- 

. 

900 

900 

DCCCC. 

One  thousand 

. 

. 

1000 

4000 

M. 

Two  thousand 

. 

. 

2000 

2000 

MM. 

e 

10 


NOTATION   AND   NUMERATION. 


LESSOI^ 

[    VI. 

Pronounce  the  numbers  meant  by  these  figures. 

1 

16 

39 

55 

68 

71 

607 

5 

14 

31 

95 

86 

91 

706 

9 

27 

37 

79 

67 

73 

831 

6 

28 

30 

59 

76 

82 

138 

7 

28 

33 

89 

66 

80 

852 

4 

22 

35 

49 

98 

92 

258 

8 

29 

54 

99 

88 

90 

528 

3 

21 

44 

69 

96 

91 

582 

2 

26 

64 

47 

52 

97 

285 

15 

20 

94 

51 

77 

100 

963 

19 

24 

74 

40 

78 

105 

369 

11 

25 

84 

48 

87 

207 

639 

18 

38 

45 

50 

60 

212 

936 

12 

34 

75 

57 

61 

321 

1000 

17 

36 

85 

58 

70 

400 

2016 

13 

32 

65 

56 

72 

505 

3478 

LE 

SSON 

VII. 

Write  in  figures  the  following  numbers  : — 
Twenty-four.     Forty-two.     Thirty-five.     Fifty-three. 
Forty-seven.     Seventy-four.     Fifty-six.     Sixty-five. 
Sixty-seven.    Seventy-six.    Seventy-eight.    Eighty-seven. 
Eighty-nine.     Ninety-eight.     Twenty-five.     Fifty. 
Fifty-two.     Thirty-six.     Sixty-three.     Seventy. 
Seventy-one.     Seventeen.     Eighty-one.     Eighteen. 
Forty-one.    Fourteen.    Fifty-one.    Fifteen.    Ninety-one. 
Nineteen.    Thirty-one.    Thirteen.    Twenty-one.    Twelve. 
Twenty-two.     Forty-four.     Thirty-three.     Ninety-nine. 
Seventy-seven.     Fifty-five.     Eighty-eight.     Sixty-six. 
Thirty-four.     Forty-three.     Fifty-seven.     Seventy-five. 
Eighty.  Sixty-eight.  Eighty-six.  One  hundred  and  sixty. 
Two  hundred  and  two.     Seven  hundred  and  four. 
One  thousand  two  hundred  and  thirty-four. 


ADDITION. 


11 


ADDITION. 


LESSON    I. 

Adding  numbers  is  finding  how  much  they  all  make 
when  reckoned  as  one  number. 

The  sum  of  two  or  more  numbers  is  that  number  which 
they  all  make  when  reckoned  as  one  number. 

When  we  count  things,  one  at  a  time,  it  is  adding  one 
every  time  to  the  numbers  we  have  counted  before. 

If  we  had  to  find  the  sum  of  several  large  numbers, 
by  counting  the  single  things  one  by  one,  it  would  take 
a  long  time.  Hence  it  is  best  to  learn  and  remember  the 
sums  of  all  small  numbers,  so  as  to  help  us  with  the 
large  ones. 

Two  cents        and       two  cents       are       four  cents. 
OO  OO  OOOO 


Three  hats      and      two  hats 


are      five  hats. 


Three  cows       and      three  cows      are  how  many  cows  ? 


Four  combs      and       five  combs  are  how  many  combs  ? 


Note  to  Teachers. — At  the  foot  of  the  following  pages  are 
exercises  showing  the  written  way  of  working  the  examples. 
The  teaclier  should  exercise  the  pupil  in  these  processes  when 
the  lesson  above  them  is  recited.  The  pupil  thus  learns  the 
simple  methods  of  Written  Arithmetic,  while  acquiring  the  first 
ideas  of  the  science. 


» 


12 

ADDITION 

LESSON 

II. 

0  and 

are 

1 

1  and 

0  are 

1 

1  and 

are 

2 

1  and 

1  are 

2 

2  and 

are 

3 

1  and 

2  are 

3 

3  and 

are 

4 

1  and 

3  are 

4 

4  and 

are 

5 

1  and 

4  are 

5 

6  and 

are 

6 

1   and 

5  are 

6 

6  and 

are 

7 

1  and 

6  are 

7 

7  and 

are 

8 

1  and 

7  are 

8 

8  and 

are 

9 

1  and 

8  are 

9 

9  and 

are 

10 

1  and 

9  are 

10 

10  and 

are 

11 

1  and 

10  are 

11 

a 


1.  Frank  had  1  cent,  and  his  father  gave  him  1  cent 
more ;  how  many  cents  had  Frank  then  ? 

Answer. — Two;  because  1  and  1  are  2. 

2.  Mary  gave  2  cents  for  an  orange,  and  1  cent  for 
candy;  how  many  cents  did  she  spend? 

3.  John  had  7  marbles,  and  his  brother  gave  him  1 
more;  how  many  had  he  then  ? 

4.  James  caught  1  fish  in  the  mill-dam,  and  5  below 
it ;  how  many  did  he  catch  ? 

5.  While  10  birds  were  on  a  tree,  another  joined  them; 
how  many  were  there  then  ? 

6.  If  you  give  8  cents  for  a  slate,  and  1  cent  for  a 
pencil,  how  much  do  you  give  for  both  ? 

7.  If  you  spell  3  words  wrong  one  day,  and  1  word  the 
next  day,  how  many  do  you  miss  in  both  days  ? 

8.  John  found  9  eggs  in  the  barn,  and  Jane  found  1; 
how  many  did  both  find  ? 

9.  How  many  persons  are  6  girls  and  1  boy? 


FOR 

THE 

SLATE 

OE    BLACKBOARD. 

1 

2 

7 

1 

10 

Ill 

6 

4 

1 

1 

1 

5 

1 

8      3      9 

1 

1 

■^ 


ADDITION. 


13 


LESSON    III. 


0  and  2  are 

2 

2  and 

0  are 

2 

1  and  2  are 

3 

2  and 

1  are 

3 

2  and  2  are 

4 

2  and 

2  are 

4 

3  and  2  are 

5 

2  and 

3  are 

5 

4  and  2  are 

6 

2  and 

4  are 

6 

5  and  2  are 

7 

2  and 

5  are 

7 

6  and  2  are 

8 

2  and 

6  are 

8 

7  and  2  are 

9 

2  and 

7  are 

9 

8  and  2  are 

10 

2  and 

8  are 

10 

9  and  2  are 

11 

2  and 

9  are 

11 

10  and  2  are 

12 

2  and  10  are 

12 

1.  In  one  lot  are  5  cows,  and  in  another  2  cows;  how 
many  cows  are  in  both  lots  ? 

2.  How  many  children  has  a  man  who  has  3  sons  and 
2  daughters  ? 

3.  Ellen  is  7  years  old,  and  Horace  is  2  years  older; 
how  old  is  Horace  ? 

4.  There  are  6  trees  in  the  garden,  and  2  in  the  front 
yard ;  how  many  are  in  both  places  ? 

5.  I  own  9  ducks,  and  Mary  2  ;  how  many  have  we? 

6.  David  gathered  2  quarts  of  chestnuts,  and  Horace 
8 ;  how  many  did  both  gather  ? 

7.  Harriet  bought  tape  for  2  cents,  and  thread  for  2 
cents ;  how  much  did  both  cost  ? 

8.  Henry  sold  4  dollars'  worth  of  produce,  and  Edward 
2  dollars*  worth ;  how  much  did  both  sell  ? 

9.  How  many  are  3  apple-trees  and  2  pear-trees  ? 

10.  How  many  animals  are  2  cows  and  7  sheep? 

11.  What  12  things  are  10  carp  and  2  trout? 


FOR  THE 

SLATE    OR 

BLACKBOARD. 

5 

2 

7       2 

9      2 

2      4      2 

7 

10 

2 

3 

2       6 

2       8 

2      2      3 

2 

2 

14 

ADDITION 

• 

-» 

LESSON 

IV. 

0  and  3 

are 

3 

3  and 

0  are     3 

1  and  3 

are 

4 

3  and 

1  are     4 

2  and  3 

are 

5 

3  and 

2  are     5 

3  and  3 

are 

6 

3  and 

3  are     6 

4  and  3 

are 

7 

3  and 

4  are     7 

5  and  3 

are 

8 

3  and 

5  are     8 

6  and  3 

are 

9 

3  and 

6  are     9 

7  and  3 

are 

10 

3  and 

7  are  10 

8  and  3 

are 

11 

3  and 

8  are  11 

9  and  3 

are 

12 

3  and 

9  are  12 

10  and  3 

are 

13 

3  and  10  are  13 

1.  Martha  visited  2  weeks  at  Uncle  John's,  and  3  at 
Uncle  Greorge's ;  how  long  were  both  visits  ? 

2.  Julia  counted  4  rooms  on  the  first  floor,  and  3  on 
the  second ;  how  many  were  on  both  floors  ? 

3.  There  are  6  chairs  in  the  parlor,  and  3  in  the  kitchen; 
how  many  chairs  are  in  both  rooms  ? 

4.  There  are  8  steps  in  the  lower  stairs,  and  3  in  the 
upper ;  how  many  steps  are  in  the  stairs  ? 

5.  Sarah  owned  7  chickens,  and  David  3  chickens; 
how  many  did  both  own  ? 

6.  If  you  earn  at  one  time  10  cents,  and  at  another  3 
cents,  how  many  cents  do  you  earn  in  all  ? 

7.  Harvey  and  Peter  bought  a  ball;  Harvey  gave  5 
cents  and  Peter  3 ;  what  did  the  ball  cost  ? 

8.  After  Robert  had  given  away  3  apples,  he  had  3 
left ;  how  many  had  he  at  first  ? 

9.  Charles  traveled  9  miles  by  steamboat  and  3  by 
stage ;  how  far  did  he  travel  ? 


FOB   THE 

SLATE 

OR    BLACKBOARD. 

2 

3 

3 
4 

6            3 

3       8 

7 
3 

3            5            3 

10       3       3 

9 
3 

3 
1 

ADDITION. 


15 


LESSON  V. 

0  and  4  are 

4 

4  and 

0  are 

4 

1  and  4  are 

5 

4  and 

1  are 

5 

2  and  4  are 

6 

4  and 

2  are 

6 

3  and  4  are 

7 

4  and 

3  are 

7 

4  and  4  are 

8 

4  and 

4  are 

8 

5  and  4  are 

9 

4  and 

5  are 

9 

6  and  4  are 

10 

4  and 

6  are 

10 

7  and  4  are 

11 

4  and 

7  are 

11 

8  and  4  are 

12 

4  and 

8  are 

12 

9  and  4  are 

13 

4  and 

9  are 

13 

10  and  4  are 

14 

4  and  10  are 

14 

1.  There  are  5  houses  on  one  side  of  the  park,  and  4 
on  the  other ;  how  many  are  on  both  sides  ? 

2.  There  were  7  boys  skating  and  4  girls  sliding  on 
the  ice ;  how  many  were  in  the  company  ? 

3.  There  were  10  turkeys  in  one  flock,  and  4  in  an- 
other ;  how  many  were  in  both  flocks  ? 

4.  Ann  saw,  from  the  window,  6  men  in  one  group, 
and  4  in  another ;  how  many  were  in  both  ? 

5.  I  saw  3  doves  alight  on  the  roof,  and  4  on  the 
ground ;  how  many  were  there  in  all  ? 

6.  Laura  had  8  pins  on  the  cushion,  and  stuck  on  it 
4  more ;  how  many  were  on  it  then  ? 

7.  Alfred  gave  9  cents  for  a  line,  and  4  for  a  hook; 
how  many  cents  did  he  give  for  both  ? 

8.  A  farmer  had  4  cows  in  a  lot,  and  put  in  2  more; 
how  many  cows  were  then  in  the  lot  ? 

9.  If  the  right  hand  has  4  fingers,  and  the  left  4 
fingers,  how  many  fingers  have  both  hands  ? 


FOR   THE 

SLATE    OR 

BLACKBOARD. 

5 
4 

4 

7 

10           4 

3  4 

4  8 

9       4      4 
4      2      4 

4 
1 

4 
0 

16 


ADDITION. 


LESSON  VI. 


0  and  5  are     5 

5  and 

0  are     5 

1  and  5  are     6 

5  and 

1  are     6 

2  and  5  are     7 

5  and 

2  are     7 

3  and  5  are     8 

5  and 

3  are     8 

4  and  5  are     9 

5  and 

4  are     9 

5  and  5  are  10 

5  and 

5  are  10 

6  and  5  are  11 

5  and 

6  are  11 

7  and  5  are  12 

5  and 

7  are  12 

8  and  5  are  13 

5  and 

8  are  13 

9  and  5  are  14 

5  and 

9  are  14 

10  and  5  are  15 

5  and  10  are  15 

1.  How  many  are  3  fingers  of  one  hand,  and  the 
fingers  and  thumb  of  the  other  ? 

2.  How  many  are  4  fingers  of  one   hand,  and  the 
fingers  and  thumb  of  the  other  ? 

3.  How  many  are  all  the  fingers  and  thumb  of  one 
hand,  and  all  of  the  other  ? 

4.  How  many  are  2  fingers  of  one  hand,  and  all  of  the 
other,  including  the  thumb  ? 

5.  How  many  are  1  finger  of  one  hand,  and  all  of  the 
other,  including  the  thumb  ? 

6.  There  are  7  tumblers  in  the  cupboard,  and  5  on  the 
table ;  how  many  are  there  in  all  ? 

7.  Frank  counted  10  freight-cars  and  5  passenger-cars 
in  a  train ;  how  many  in  all  ? 

8.  In  an  omnibus,  6  persons  were  on  one  side,  and  5  on 
the  other ;  how  many  were  in  the  omnibus  ? 

9.  I  saw  9  barrels  standing  on  their  ends,  and  5  lying 
on  their  sides ;  how  many  in  all  ? 


FOR   THE 

SLATE    OR   BLACKBOARD. 

5 
3 

4 
5 

5       2 
5       5 

5      7     10      5      9 
15       5      6      5 

ADDITION. 


17 


LESSON  VII. 


0  and  6  are     6 

6  and 

0  are     6 

1  and  6  are     7 

6  and 

1  are     7 

2  and  6  are     8 

6  and 

2  are     8 

3  and  6  are     9 

6  and 

3  are     9 

4  and  6  are  10 

6  and 

4  are  10 

5  and  6  are  11 

6  and 

5  are  11 

6  and  6  are  12 

6  and 

6  are  12 

7  and  6  are  13 

6  and 

7  are  13 

8  and  6  are  14 

6  and 

8  are  14 

9  and  6  are  15 

6  and 

9  are  15 

0  and  6  are  16 

6  and  10  are  16 

1.  The  white  cow  gives  4  quarts  of  milk,  and  the  red 
cow  6  quarts ;  how  much  do  both  give  ? 

2.  Mr.  Jones  had  8  trees  before  his  house,  and  he 
planted  6  more  3  how  many  were  there  then  ? 

3.  Sarah's  mother  had  6  cups  and  saucers,  and  she 
bought  6  more ;  how  many  had  she  then  ? 

4.  She  bought  3  brooms  at  one  time,  and  6  at  another ; 
how  many  in  all  did  she  buy  ? 

5.  Carrie  counted  7  large  plates  on  the  table,  and  6 
small  ones ;  how  many  did  she  count  ? 

6.  George  caught  in  his  traps  2  mice  one  day,  and  the 
next  day  6  more ;  how  many  did  he  catch  ? 

7.  Susan  baked  at  one  time  5  cakes  and  6  pies;  how 
many  things  did  she  bake  at  that  time  ? 

8.  Oscar  went  a  fishing,  and  caught  9  trout  and  6 
perch ;  how  many  fishes  did  he  catch  ? 

9.  Daniel  gave  10  cents  for  a  bottle  of  ink,  and  6  cents 
for  pens ;  what  did  both  cost  ? 

FOB   THE    SLATE    OR    BLACKBOARD. 

46667656   10   66 
68636269   610 


&- 


18 


ADDITION. 


LESSON  VIII. 


0  and  7  are     7 

7  and 

0  are     7 

1  and  7  are     8 

7  and 

1  are     8 

2  and  7  are     9 

7  and 

2  are     9 

3  and  7  are  10 

7  and 

3  are  10 

4  and  7  are  11 

7  and 

4  are  11 

6  and  7  are  12 

7  and 

5  are  12 

6  and  7  are  13 

7  and 

6  are  13 

7  and  7  are  14 

7  and 

7  are  14 

8  and  7  are  15 

7  and 

8  are  15 

9  and  7  are  16 

7  and 

9  are  16 

10  and  7  are  17 

7  and 

10  are  17 

1.  Oliver  had  5  marbles,  and  bought  7  more;   how 
many  had  he  then  ? 

2.  Martin  saw  on  the  wharf  9  barrels  of  molasses,  and 
7  of  oil }  how  many  barrels  did  he  see  ? 

3.  Ada  saw  at  a  drug-store  6  bottles  in  one  window, 
and  7  in  another;  how  many  did  she  see? 

4.  John  drives  3  cows  to  pasture,  and  James  7;  how 
many  cows  do  both  drive  ? 

5.  Anna  picked  7  red  apples  and  7  yellow  ones;  how 
many  apples  did  she  pick  ? 

6.  Jacob  saw  in  a  lot  10  sheep  lying  down,  and  7  stand- 
ing ;  how  many  sheep  did  he  see  ? 

7.  In  the  next  lot  he  saw  4  cows  standing,  and  7  lying 
down ;  how  many  cows  did  he  see  ? 

8.  He  saw  7  swallows  fly  out  of  a  barn,  and  2  others 
fly  in ;  how  many  did  he  see  ? 

9.  Mary  made  8  sheets  and  7  pillow-cases;  how  many 
pieces  were  these  ? 


FOR 

THE 

SLATE    OR 

BLACKBOARD. 

5 

7 

6 

7 

7 

10 

7 

2 

7 

1 

7 

7 

9 

7 

3 

7 

7 

4 

7 

8 

7 

0 

ADDITION. 


19 


LESSON  IX. 


0  and  8 

are 

8 

8 

and 

0  are     8 

1  and  8 

are 

9 

8 

and 

1  are     9 

2  and  8 

are 

10 

8 

and 

2  are  10 

3  and  8 

are 

11 

8 

and 

3  are  11 

4  and  8 

are 

12 

8 

and 

4  are  12 

5  and  8 

are 

13 

8 

and 

5  are  13 

6  and  8 

are 

14 

8 

and 

6  are  14 

7  and  8 

are 

15 

8 

and 

7  are  15 

8  and  8 

are 

16 

8 

and 

8  are  16 

9  and  8 

are 

17 

8 

and 

9  are  17 

10  and  8 

are 

18 

8 

and 

10  are  18 

1.  Andrew's  school  has  4  weeks'  vacation  in  winter, 
and  8  in  summer ;  how  many  has  it  in  a  year  ? 

2.  How  many  fingers  are  8  fingers  and  2  thumbs  ? 

3.  Edwin  dug  5  potatoes  from  one  hill,  and  8  from 
another ;  how  many  did  he  dig  from  both  ? 

4.  Seven  rolls  papered  the  dining-room,  and  8   the 
parlor ;  how  many  rolls  did  both  rooms  take  ? 

5.  Mrs.  Hill  made  6  pounds  of  butter  one  week,  and 
8  the  next ;  how  many  pounds  in  both  weeks  ? 

6.  The  family  ate,  in  a  week,  9  pounds  of  beef,  and  8 
of  mutton ;  how  much  meat  was  that  ? 

7.  They  ate  10  loaves  of  bread  in  one  week,  and  8  in 
another ;  how  many  did  they  eat  in  both  weeks  ? 

8.  How  many  cents  are  8  cents  and  1  cent  ? 

9.  John's  coat  has  8  buttons  on  the  right  side,  and  8 
on  the  left ;  how  many  are  on  both  sides  ? 

10.  Harry   brought   in    3   bucketfuls   of   water,  and 
Richard  8 ;  how  many  did  both  bring  in  ? 


20 


ADDITION. 


LESSON    X. 


0  and  9  are     9 

9  and 

0  are    9 

1  and  9  are  10 

9  and 

1  are  10 

2  and  9  are  11 

9  and 

2  are  11 

3  and  9  are  12 

9  and 

3  are  12 

4  and  9  are  13 

9  and 

4  are  13 

5  and  9  are  14 

9  and 

5  are  14 

6  and  9  are  15 

9  and 

6  are  15 

7  and  9  are  16 

9  and 

7  are  16 

8  and  9  are  17 

9  and 

8  are  17 

9  and  9  are  18 

9  and 

9  are  18 

10  and  9  are  19 

9  and 

10  are  19 

1.  Joseph  Henderson  has  6  letters  in  the  first  name, 
and  9  in  the  second ;  how  many  in  both  ? 

2.  In  Elm  Street  are  8  gas-lights  on  one  side,  and  9  on 
the  other;  how  many  are  on  both  sides  ? 

3.  Herman   planted  5  rows  of  beets,  and  9  rows  of 
onions;  how  many  rows  in  all  did  he  plant? 

4.  In  the  hall  there  are  10  hat-hooks  on  one  side,  and 
9  on  the  other;  how  many  are  on  both  sides? 

5.  Willie  learned  4  letters  one  day,  and  9  the  next; 
how  many  did  he  learn  in  both  days  ? 

6.  If  you  give  7  cents  for  a  top,  and  9  cents  for  fire- 
crackers, how  much  do  both  cost  you? 

7.  Some  boys,  "  playing  soldier,'^  had  3  officers,  and  9 
not  officers ;  how  many  boys  were  playing  ? 

8.  Nine  girls  were  swinging,  and  9  jumping  the  rope; 
how  many  girls  were  playing  ? 

9.  Emily's  father  brought  home  2  pounds  of  tea,  and 
9  of  sugar;  how  much  weight  were  both  ? 


FOR   THE 

SLATE    OR 

BLACKBOARD. 

6 

9 

5      9 

4      9 

3       9       2 

9 

9 

9 

8 

9     10 

9      7 

9      9      9 

1 

0 

ADDITION. 


21 


LESSON    XI. 


0  and  10  are  10 

10  and 

0  are  10 

1  and  10  are  11 

10  and 

1  are  11 

2  and  10  are  12 

10  and 

2  are  12 

3  and  10  are  13 

10  and 

3  are  13 

4  and  10  are  14 

10  and 

4  are  14 

5  and  10  are  15 

10  and 

5  are  15 

6  and  10  are  16 

10  and 

6  are  16 

7  and  10  are  17 

10  and 

7  are  17 

8  and  10  are  18 

10  and 

8  are  18 

9  and  10  are  19 

10  and 

9  are  19 

0  and  10  are  20 

10  and 

10  are  20 

1.  If  you  had  3  cents,  and  your  father  gave  you  a 
10-cent-piece,  how  much  would  you  have? 

2.  If  you  had  a  5-cent-piece,  and  a  man  gave  you  a 
10-cent-piece,  how  much  would  you  have  ? 

3.  If  you  had  a  10-cent-piece,  and  earned  another, 
how  much  money  would  you  have  ? 

4.  On    New-Year's   Day  Ernest   spent   8   cents,  and 
Frances  10  cents;  how  much  did  both  spend? 

5.  Christmas  morning,  Frank's  stocking  had  9  sugar- 
kisses,  and  Ada's  10;  how  many  had  both? 

6.  In  the  spring  one  hen  came  cut  with  6  chickens, 
and  another  with  10;  how  many  had  both? 

7.  Edwin    built  a  little   oven  of  10   bricks,  and  its 
chimney  of  4  bricks ;  how  many  did  he  use  ? 

8.  He  baked  in  it  2  pears  and  10  apples  at  a  time; 
how  many  things  did  he  bake  at  a  time  ? 

9.  Lucius  had  7  dollars,  and  sold  his  colt  for  10  dol- 
lars ;  how  much  money  had  he  then  ? 


FOR   THE    SLATE    OR   BLACKBOARD. 

3 

10 

10        8     10        6     10        2 

10 

10 

10 

5 

10      10       9      10       4      10 

7 

1 

22 

ADDITION. 

» 

LESSON 

XII. 

REVIEW 

'. 

1. 

How  many  are 

2  and 

3? 

3  and 

2? 

4  and 

2? 

2. 

How  many  are 

2  and 

4? 

5  and 

2? 

6  and 

3? 

3. 

How  many  are 

2  and 

5? 

3  and 

6? 

8  and 

2? 

4. 

How  many  are 

2  and 

7? 

2  and 

8? 

7  and 

2? 

5. 

How  many  are 

2  and  10? 

9  and 

2? 

10  and 

2? 

6. 

How  many  are 

2  and 

9? 

4  and 

6? 

6  and 

2? 

7. 

How  many  are 

2  and 

6? 

6  and 

4? 

3  and 

5? 

8. 

How  many  are 

7  and 

3? 

5  and 

3? 

3  and 

7? 

9. 

How  many  are 

4  and 

3? 

3  and 

8? 

3  and 

4? 

10. 

How  many  are 

8  and 

3? 

3  and 

9? 

10  and 

3? 

11. 

How  many  are 

9  and 

3? 

3  and  10? 

5  and 

4? 

12. 

How  many  are 

4  and  10? 

4  and 

5? 

10  and 

4? 

13. 

How  many  are 

7  and 

4? 

9  and 

4? 

4  and 

9? 

14. 

How  many  are 

4  and 

7? 

4  and 

4? 

8  and 

4? 

15. 

How  many  are 

3  and 

3? 

4  and 

8? 

2  and 

2? 

16. 

How  many  are 

5  and 

5? 

6  and 

5? 

5  and 

6? 

17. 

How  many  are 

10  and 

5? 

5  and 

8? 

5  and  10?  1 

18. 

How  many  are 

8  and 

5? 

5  and 

7? 

9  and 

5? 

19. 

How  many  are 

5  and 

9? 

7  and 

5? 

6  and 

6? 

20. 

How  many  are 

10  and 

6? 

6  and  10? 

7  and 

6? 

21. 

How  many  are 

6  and 

7? 

8  and 

6? 

6  and 

8? 

22. 

How  many  are 

6  and 

9? 

9  and 

6? 

7  and 

7? 

23. 

How  many  are 

9  and 

7? 

7  and 

9? 

10  and 

7? 

24. 

How  many  are 

8  and 

7? 

7  and  10? 

7  and 

8? 

25. 

How  many  are 

8  and 

8? 

10  and 

8? 

8  and 

9? 

26. 

How  many  are 

9  and 

8? 

9  and 

9? 

10  and 

9? 

27. 

How  many  are 

1  and 

2  and  3? 

28. 

How  many  are 

2  and 

3  and  4  ? 

29. 

How  many  are 

3  and 

4  and  5  ? 

30 

How  many  are 

4  and 

5  and  6  ? 

31. 

How  many  are 

4  and 

6  and  7  ? 

32. 

How  many  are 

1  and 

3  and  7  and  8  ? 

33. 

How  many  are 

2  and 

7  and  8  and  9  ? 

34. 

How  many  are 

10  and  10  and  5  and  3  ? 

»  — 

c 

— a 

I  ADDITION.  23 


LESSON    XIII. 

PROMISCUOUS   EXERCISES. 

1.  If  you  give  3  cents  for  tape,  3  for  thread,  and  4  for 
needles,  how  much  do  you  give  for  all  ? 

2.  If  you  sell  eggs  for  6  cents,  a  cabbage  for  5  cents, 
and  currants  for  5  cents,  how  many  cents  do  you  get  for 
all? 

3.  John's  hat  cost  2  dollars,  his  shoes  2  dollars,  and 
the  rest  of  his  suit  7  dollars;  what  did  his  whole  suit 
cost? 

4.  I  gave  4  dimes  for  spice,  2  dimes  for  salt,  and  1 
dime  for  pepper;  how  much  did  I  give  for  all  ? 

5.  Jane  saw  7  swallows  come  out  of  the  barn,  then  5, 
then  3 ;  how  many  did  she  see  in  all  ? 

6.  Harvey  went  a  fishing  3  times;  the  first  time  he 
caught  8  fishes,  the  next  6,  and  the  next  3 ;  how  many 
in  all  ? 

7.  Samuel  found  4  hen's  nests;  in  the  first  were  2 
eggs,  in  the  next  4,  in  the  next  7,  and  in  the  next  5; 
how  many  in  all  ? 

8.  A  little  girl  had  three  names;  in  the  first  were  4 
letters,  in  the  second  7,  and  in  the  last  8 ;  how  many 
letters  made  her  name  ? 

9.  Nine  birds  were  on  a  tree;  then  6  joined  them, 
then  5  more ;  how  many  were  then  on  the  tree  ? 

10.  Ten  doves  were  on  the  ground,  5  on  the  fence,  and 
6  on  the  roof;  how  many  in  all  ? 

11.  In  Kate's  garden  were  8  roses,  6  pinks  and  3 
dahlias ;  how  many  flowers  were  there  ? 

12.  In  the  hall  were  10  caps  in  one  row,  8  in  another, 
and  6  in  another;  how  many  in  all? 

13.  In  the  orchard  are  9  apple-trees,  7  pear-trees,  and 
5  plum-trees ;  how  many  trees  are  these  ? 

14.  If  there  are  5  fingers  on  the  right  hand,  5  on  the 
left,  5  toes  on  the  right  foot,  and  5  on  the  left,  how  many 
fingers  and  toes  are  there  ? 


24 

ADDITION. 

« 

LESSON   xiy. 

Carry  out  eacli  following  line  as  indicated. 

1. 

How  many  are  1  and  10? 

land  20? 

1  and  30?&c. 

2 

2  and  10? 

2  and  20? 

2  and  30? 

2and40?&c. 

d. 

3  and  10? 

3  and  20? 

3  and  30  ? 

3  and40?&c. 

4. 

5  and  10? 

5  and  20? 

5  and  30? 

5and40?&c. 

5. 

7  and  10? 

7  and  20? 

7  and  30? 

7  and40?&c. 

6. 

8  and  10? 

8  and  20? 

8  and  30? 

8  and  40  ?  &c. 

7. 

9  and  10? 

9  and  20? 

9  and  30? 

9  and40?&c. 

8. 

land  11? 

1  and  21? 

1  and  31? 

1  and41?&c. 

9. 

2  and  11? 

2  and  21? 

2  and  31? 

2and41?&c. 

10. 

4  and  11? 

4  and  21? 

4  and  31? 

4  and  41  ?  &c. 

11. 

5  and  11  ? 

5  and  21? 

5  and  31? 

5and41?&c. 

12. 

6  and  11? 

6  and  21? 

6  and  31? 

6and41?&c. 

13. 

7  and  11? 

7  and  21? 

7  and  31? 

7  and41?&c. 

14. 

8  and  11? 

8  and  21? 

8  and  31? 

8  and41?&c. 

15 

1  and  12? 

land  22? 

land  32? 

1  and42?&c. 

16. 

2  and  12? 

2  and  22? 

2  and  32? 

2and42?&c. 

17. 

3  and  12? 

3and^? 

3  and  32? 

3  and42?&c. 

18. 

4  and  12? 

4  and  22? 

4  and  32? 

4and42?&c. 

19. 

6  and 

2? 

6  and  12? 

6  and  22? 

6  and  32  ?  &c. 

20. 

8  and 

2? 

8  and  12? 

8  and  22? 

8and32?&c. 

21. 

9  and 

2? 

9  and  12? 

9  and  22? 

9  and  32  ?  &c. 

22. 

1  and 

3? 

land  13? 

1  and  23? 

1  and  33  ?  &c. 

23. 

3  and 

3? 

3  and  13? 

3  and  23? 

3  and  33  ?  &c. 

24. 

5  and 

3? 

5  and  13? 

5  and  23? 

5  and  33  ?  &c. 

25. 

6  and 

3? 

6  and  13  ? 

6  and  23? 

6  and  33  ?  &c. 

26. 

7  and 

3? 

7  and  13? 

7  and  23? 

7and33?&c. 

27. 

8  and 

3? 

8  and  13? 

8  and  23? 

8  and33?&c. 

28. 

9  and 

3? 

9  and  13? 

9  and  23? 

9  and  33  ?  &c. 

29. 

2  and 

4? 

2  and  14? 

2  and  24? 

2and34?&c. 

30. 

3  and 

4? 

3  and  14? 

3  and  24? 

3  and34?&c. 

31. 

4  and 

4? 

4  and  14? 

4  and  24? 

4  and34?&c. 

32. 

5  and 

4? 

5  and  14? 

5  and  24? 

5and34?&c. 

33. 

6  and 

4? 

6  and  14? 

6  and  24? 

6and34?&c. 

34. 

8  and 

4? 

8  and  14? 

8  and  24? 

8  and34?&c. 

35. 
g 

9  and 

4? 

9  and  14? 

9  and  24? 

9and34?<fec. 

s 

ADDITION. 

9 

25 

LESSON    XV. 

1. 

How  many  are  1  and  5  ? 

1  and  15  ? 

1  and  25  ?  &c. 

2. 

3  and  5  ? 

3  and  15  ? 

3  and  25  ? 

3  and  35  ?  &c. 

3. 

4  and  5  ? 

4  and  15  ? 

4  and  25  ? 

4  and  35  ?  &c. 

4. 

5  and  5  ? 

5  and  15? 

5  and  25  ? 

5  and  35  ?  &c.  ' 

5. 

6  and  5  ? 

6  and  15  ? 

6  and  25  ? 

6  and  35  ?  &c. 

6. 

7  and  5  ? 

7  and  15  ? 

7  and  25  ? 

7  and  35  ?  &c. 

7. 

9  and  5  ? 

9  and  15  ? 

9  and  25  ? 

9  and  35  ?  &c. 

8. 

3  and  6  ? 

3  and  16  ? 

3  and  26  ? 

3  and  36  ?  &c. 

9. 

4  and  6  ? 

4  and  16  ? 

4  and  26  ? 

4  and  36  ?  &c. 

10. 

5  and  6  ? 

5  and  16  ? 

5  and  26  ? 

5  and  36  ?  &c. 

11. 

6  and  6  ? 

6  and  16  ? 

6  and  26  ? 

6  and  36  ?  &c. 

12. 

7  and  6  ? 

7  and  16  ? 

7  and  26  ? 

7  and  36  ?  &c. 

13. 

8  and  6  ? 

8  and  16? 

8  and  26  ? 

8  and  36  ?  &c. 

14. 

9  and  6  ? 

9  and  16  ? 

9  and  26  ? 

9  and  36  ?  &c. 

15. 

2  and  7  ? 

2  and  17  ? 

2  and  27  ? 

2  and  37  ?  &c. 

16. 

4  and  7  ? 

4  and  17  ? 

4  and  27  ? 

4*  and  37  ?  &c. 

17. 

5  and  7  ? 

5  and  17  ? 

5  and  27  ? 

5  and  37  ?  &c. 

18. 

6  and  7  ? 

6  and  17  ? 

6  and  27  ? 

6  and  37  ?  &c. 

19. 

7  and  7  ? 

7  and  17  ? 

7  and  27  ? 

7  and  37  ?  &c. 

20. 

8  and  7  ? 

8  and  17  ? 

8  and  27  ? 

8  and  37  ?  &c. 

21. 

9  and  7  ? 

9  and  17  ? 

9  and  27  ? 

9  and  37  ?  &c. 

22. 

2  and  8  ? 

2  and  18  ? 

2  and  28  ? 

2  and  38  ?  &c. 

23. 

3  and  8  ? 

3  and  18  ? 

3  and  28  ? 

3  and  38  ?  &c. 

24. 

5  and  8  ? 

5  and  18  ? 

5  and  28  ? 

5  and  38  ?  &c. 

25. 

6  and  8  ? 

6  and  18  ? 

6  and  28  ? 

6  and  38  ?  &c. 

26. 

7  and  8  ? 

7  and  18  ? 

7  and  28  ? 

7  and  38  ?  &c. 

27. 

8  and  8  ? 

8  and  IS  ? 

8  and  28  ? 

8  and  38  ?  &c. 

28. 

9  and  8  ? 

9  and  18  ? 

9  and  28  ? 

9  and  38  ?  &c. 

29. 

2  and  9  ? 

2  and  19  ? 

2  and  29  ? 

2  and  39  ?  &c. 

30. 

3  and  9  ? 

3  and  19  ? 

3  and  29  ? 

3  and  39  ?  &c. 

31. 

4  and  9  ? 

4  and  19  ? 

4  and  29  ? 

4  and  39  ?  &c. 

32. 

5  and  9  ? 

5  and  19  ? 

5  and  29  ? 

5  and  39  ?  &c. 

33. 

6  and  9  ? 

6  and  19  ? 

6  and  29  ? 

6  and  39  ?  &c. 

34. 

7  and  9  ? 

7  and  19  ? 

7  and  29  ? 

7  and  39  ?  &c. 

35. 

8  and  9  ? 

8  and  19  ? 

8  and  29  ? 

8  and  39  ?  &c. 

36. 

9  and  9  ? 

9  and  19  ? 

9  and  29  ? 

9  and  39  ?  &c. 

26  ADDITION. 


LESSON    XVL 

COUNTING   BY  TWOS. 

Now  make  twenty  marks  upon  the  slate  or  blackboard, 
and  separate  them  into  twos  with  commas ;  thus  : — 

I  M  hi  \>\  \>\  \>\  \,\  \>\  \,\  \,\  I 

Count  this  row  by  twosj  saying  two^  four,  six,  &c.  If 
you  cannot  do  this  at  first,  then  begin  by  saying  the 
omitted  number  mentally,  and  the  desirca  number  aloud; 
thus, — one,  two,  three,  four,  &c.  When  you  have 
learned  to  do  this,  omit  saying  any  number  mentally,  and 
count  only  by  twos. 

Now  separate  this  row  of  marks  as  follows : — 

M  M  I.I  I.I  I.I  I.I  I.I  I.I  I.I  I.I  I 

Count  this  row  from  1,  by  ticosj  saying  one,  three,  jive^ 
seven,  &c. 

Note  to  Teachers. — Make  this  a  blackboard  exercise,  till 
the  pupil  can  readily  count  a  small  number  by  twos.  Care 
should  be  taken  not  to  press  it  to  high  numbers  at  first,  defer- 
ring that  till  the  pupil  is  more  advanced.  When  the  blackboard 
exercise  has  become  familiar,  then  make  a  pile  of  books,  the 
backs  and  edges  alternating  to  assist  the  eye,  and  let  the  pupil 
count  them  by  twos,  spacing  them  off  with  his  fingers.  Then 
use  coins  in  piles  of  twos,  desks,  &c.,  till  the  art  is  acquired. 


LESSON    XVII. 

When  you  add  columns  of  figures,  you  should  only 
state  the  results  as  you  go,  doing  the  addition  silently  in 
4  the  mind.     Thus,  in  this  example,  you 

2  should  not  say  in  full   1  and  2  are  3, 

1  and  4   are  7;  but  thus:   1,   8,  7;   and 

—  write  the  last  result,  or  sum,  under  the 

7  line. 


fi 

— -  ~~ 

W 

ADDITION. 

27 

(1) 

(2) 

G^) 

(4) 

(5) 

(6) 

(7) 

(8) 

(9) 

(10) 

2 

1 

o 

2 

3 

3 

2 

3 

3 

3 

2 

3 

3 

2 

3 

3 

0 

4 

2 

4 

1 

1 

1 

2 

2 

3 

2 

0 

4 

3 

(11) 

(12) 

as) 

a4) 

(15) 

(16) 

(17) 

(18) 

(19) 

(20) 

4 

2 

3 

4 

4 

3 

5 

6 

5 

6 

3 

2 

1 

2 

3 

3 

4 

4 

4 

4 

2 

2 

4 

0 

3 

3 

3 

4 

4 

4 

1 

2 

3 

5 

2 

3 

1 

1 

2 

3 

(21) 

(22) 

(23) 

(24) 

(25) 

(26) 

(27) 

(28) 

(29) 

(30) 

4 

5 

4 

5 

5 

5 

7 

6 

5 

3 

4 

4 

4 

4 

5 

5 

1 

7 

7 

3 

4 

4 

5 

5 

5 

6 

0 

3 

4 

4 

4 

6 

4 

5 

4 

5 

6 

4 

3 

7 

(31) 

(32) 

(33) 

(34) 

(35) 

(36) 

(37) 

(38) 

(39) 

(40) 

2 

2 

2 

3 

3 

4 

6 

6 

7 

1 

2 

2 

1 

2 

4 

1 

1 

0 

0 

2 

2 

3 

3 

3 

3 

5 

6 

7 

8 

3 

1 

2 

1 

2 

2 

1 

1 

0 

0 

4 

2 

3 

4 

3  , 

5 

6 

7 

8 

8 

5 

1 

2 

1 

2 

JL 

1 

1 

1 

2 

6 

(41) 

(42) 

(43) 

(44) 

m 

(48) 

(47) 

(48) 

(49) 

(50) 

1 

3 

4 

5 

4 

9 

7 

6 

8 

9 

0 

0 

4 

4 

3 

8 

8 

7 

4 

8 

2 

5 

3 

3 

2 

1 

9 

8 

6 

7 

0 

1 

3 

2 

1 

2 

0 

0 

2 

6 

4 

6 

2 

1 

0 

1 

1 

8 

4 

5 

0 

2 

2 

3 

1 

3 

7  * 

7 

1 

4 

6 

9 

0 

5 

6 

5 

6 

6 

5 

3 

7 

1 

9 

7 

9 

4 

2 

1 

3 

2 

e 


28 


SUBTRACTION. 


SUBTRACTION. 


LESSON    I. 


Subtracting  from  a  number  is  making  it  less  by 
taking  away  a  part  of  it. 

When  we  subtract  from  a  number,  we  wisb  to  find  bow 
much  remains  after  taking  away  a  part. 

The  remainder,  or  difference,  is  what  is  left  after  sub- 
tracting. 

1.  If  1  of  two  trees  falls,         1  tree  is  left  standing. 


One  taken  from  two  leaves  how  many? 

2.  If  1  of  3  balls  is  taken,  how  many  are  left  ? 


One  from  three  leaves  how  many? 

3.  If  2  of  4  cars  be  taken,  how  many  will  be  left? 


Two  from  four  leaves  how  many? 

4.  If  3  of  5  tumblers  break,  how  many  are  whole? 


Three  from  five  leaves  how  many  ? 
5.  If  2  of  6  chairs  are  thrown  down,  how  many  re- 
main standing  ? 


Two  from  six  leaves  how  many? 
6.  Four  from  ten  leaves  how  many  ? 


SUBTRACTION. 

29 

LESSON    11. 

1  from  0, 

impossible. 

1  from 

1  leaves  0 

0  from 

1  leaves  1 

1  from 

2  leaves  1 

1  from 

2  leaves  1 

1  from 

3  leaves  2 

2  from 

3  leaves  1 

1  from 

4  leaves  3 

3  from 

4  leaves  1 

1  from 

5  leaves  4 

4  from 

5  leaves  1 

1  from 

6  leaves  5 

5  from 

6  leaves  1 

1  from 

7  leaves  6 

6  from 

7  leaves  1 

1  from 

8  leaves  7 

7  from 

8  leaves  1 

1  from 

9  leaves  8 

8  from 

9  leaves  1 

1  from  10  leaves  9 

9  from  10  leaves  1 

1.  Albert  had,  2  chickens,  and  1  of  them  died;  how 
many  had  he  left? 

Answer. — 1,  because  1  from  2  leaves  1. 

2.  Julia  had  5  cents,  and  spent  1  of  them;  how  many 
cents  had  she  left? 

3.  There  were  7  doves  on  the  barn,  and  1  flew  away; 
how  many  remained  ? 

4.  Thomas  caught  3  mice,  but  1  of  them  escaped; 
how  many  were  left  ? 

5.  John  brought  home  6  eggs,  but  found  1  of  them 
broken ;  how  many  whole  eggs  remained  ? 

6.  Henry  had  4  apples,  and  gave  1  of  them  away; 
how  many  had  he  left  ? 

7.  Lucy  put  9  pins  on  the  cushion,  and  then  took  one 
of  them  to  pin  her  shawl ;  how  many  remained  on  the 
cushion  ? 

8.  There  were  8  horses  in  a  field,  but  1  jumped  out; 
how  many  remained  in  the  field  ? 


30 


SUBTRACTION. 


-» 


LESSON    III. 


2  from  less 

,  iqapossible. 

2  from    2  leaves  0 

0  from    2  leaves  2 

2  from    3  leaves  1 

1  from    3  leaves  2 

2  from    4  leaves  2 

2  from    4  leaves  2 

2  from    5  leaves  3 

3  from    5  leaves  2 

2  from    6  leaves  4 

4  from    6  leaves  2 

2  from    7  leaves  5 

5  from    7  leaves  2 

2  from    8  leaves  6 

6  from    8  leaves  2 

2  from    9  leaves  7 

7  from    9  leaves  2 

2  from  10  leaves  8 

8  from  10  leaves  2 

2  from  11  leaves  9 

9  from  11  leaves  2 

1.  Sarah^s  rose-bush  had  4  roses,  and  she  picked  2  of 
them ;  how  many  remained  on  the  bush  ? 

2.  Jacob  is  6  years  old,  and  his  brother  2  years  old; 
how  much  older  is  Jacob  than  his  brother? 

3.  Jane  bought  8  yards  of  calico,  and  cut  off  2  for 
aprons ;  how  many  yards  were  left  ? 

4.  There  were  10  houses  on  one  side  of  the  street,  and 
2  were  burned ;  how  many  remained  ? 

5.  Mary  found  3  eggs  in  the  hen's  nest,  and  took  2  of 
them ;  how  many  were  left  ? 

6.  There  were  5  children  in  a  family,  and  2  of  them 
died ;  how  many  remained  ? 

7.  There  were  9  boys  playing  ball,  but  2  of  them  went 
home;  how  many  remained  ? 

8.  If  7  chairs  are  in  a  room,  and  you  take  out  2  of 
them,  how  many  will  be  left? 

9.  There  were  11  trees  in  the  orchard,  but  the  wind 
blew  down  2  of  them ;  how  many  remained  ? 


FOB 

THE 

SLATE 

OR    BLACKrOARD. 

4 

6 

8 

10 

3 

5 

9 

7 

11 

2 

rk 

2 

2 

2 

2 

2 

2 

2 

2 

2 

SUBTRACTION. 


31 


LESSON    IV. 


3  from  lesS; 

impossible. 

3  from    3  leaves  0 

0  from    3  leaves  3 

3  from    4  leaves  1 

1  from    4  leaves  3 

3  from    5  leaves  2 

2  from    5  leaves  3 

3  from    6  leaves  3 

3  from    6  leaves  3 

3  from    7  leaves  4 

4  from    7  leaves  3 

3  from    8  leaves  5 

5  from    8  leaves  3 

3  from    9  leaves  6 

6  from    9  leaves  3 

3  from  10  leaves  7 

7  from  10  leaves  3 

3  from  11  leaves  8 

8  from  11  leaves  3 

3  from  12  leaves  9 

9  from  12  leaves  3 

1.  If  you  have  5  cents  in  one  pocket,  and  3  in  another, 
how  many  more  are  in  one  than  in  the  other  ? 

2.  If  there  ^re  7  boys  and  3  girls  in  a  class,  how  many 
more  boys  than  girls  are  in  the  class  ? 

Answer. — As  many  more  as  7  persons  are  more  than 
3  persons ',  that  is,  4  more. 

3.  How  many  more  animals  are  in  a  field  containing 
12  cows,  than  in  one  containing  3  horses  ? 

4.  One  town  is  3  miles  distant,  and  another  9,  in  the 
same  direction ;  how  far  apart  are  the  towns  ? 

5.  I  left  home  with  11  dollars,  and  returned  with  3 
dollars ;  how  many  dollars  did  I  spend  ? 

6.  John  caught  8  fishes,  but  3  were  so  small  that  he 
put  them  back ;  how  many  did  he  keep  ? 

7.  He  owed  James  10  cents,  and  paid  him  3  cents; 
how  many  cents  did  he  still  owe? 

8^.  A  man  carried  6  bushels  of  potatoes  to  market, 
and  sold  3 ;  how  many  had  he  to  carry  home  ? 


FOR 

THE 

SLATE 

OR    BLACKBOARD. 

5 

7 

12 

9 

11 

8          10            6 

4 

3 

3 

3 

3 

3 

3 

3        3        3 

3 

3 

,., 

~~~~ 

— 

—     —      — 

"~~ 

X 

32 

SUBTRACTION. 

LESSON  V. 

4  from  less 

impossible. 

4  from 

4  leaves  0 

0  from     4  leaves  4 

4  from 

5  leaves  1 

1  from     5  leaves  4 

4  from 

6  leaves  2 

2  from     6  leaves  4 

4  from 

7  leaves  3 

3  from     7  leaves  4 

4  from 

8  leaves  4 

4  from     8  leaves  4 

4  from 

9  leaves  5 

5  from     9  leaves  4 

4  from 

10  leaves  6 

6  from  10  leaves  4 

4  from  11  leaves  7 

7  from  11  leaves  4 

4  from 

12  leaves  8 

8  from  12  leaves  4 

4  from  13  leaves  9 

9  from  13  leaves  4 

1.  Harriet  had  a  party  of  10,  but  4  left  early  in  tbe 
evening ;  how  many  stayed  ? 

2.  How  many  more  are  6  days  than  4  days  ? 

3.  The  parlor  has  8  chairs,  and  the  dining-room  4; 
how  many  more  has  one  than  the  other  ? 

4.  How  many  more  letters  has  John  Dascomb  in  his 
jsecond  name  than  in  his  first  ? 

5.  A  man  lost  the  thumb  of  one  hand;   how  many 
more  members  had  the  whole  hand  then  ? 

6.  Of  12  plates,  4  got  broken ;  how  many  kept  whole  ? 

7.  The  upper  sash  has  4  panes,  and  the  lower  4 ;  how 
many  more  panes  has  one  than  the  other  ? 

8.  James  caught  4  fishes  one  day,  and  11  the  next; 
how  many  more  the  last  time  than  the  first  ? 

9.  His  hooks  cost  4  cents,  and  his  line  13  cents ;  how 
much  less  did  the  hooks  cost  than  the  line  ? 

10.  Harry  had  9  cents,  and  gave  4  for  an  orange; 
how  many  cents  had  he  left  ? 


FOR 

THE 

SLATE 

OR   BLACKBOARD. 

10 

6 

8 

7 

5 

12      4      11 

13 

9 

4 

4 

4 

4 

4 

4      4        4 

4 

4 

SUBTRACTION. 


33 


LESSOiN  VI. 


5  from  less, 

impossible 

5  from 

5  leaves  0 

0  from 

5  leaves  5 

5  from 

6  leaves  1 

1  from 

6  leaves  5 

5  from 

7  leaves  2 

2  from 

7  leaves  5 

5  from 

8  leaves  3 

3  from 

8  leaves  5 

5  from 

9  leaves  4 

4  from 

9  leaves  5 

5  from 

10  leaves  5 

5  from 

10  leaves  5 

5  from 

11  leaves  6 

6  from 

11  leaves  5 

5  from 

12  leaves  7 

7  from 

12  leaves  5 

5  from 

13  leaves  8 

8  from 

13  leaves  5 

5  from 

14  leaves  9 

.    9  from 

14  leaves  5 

1.  A  man  had  8  dollars,  and  paid  a  debt  of  5  dollars; 
how  many  dollars  had  he  left  ? 

2.  A  man  owned  11  acres  of  land,  and  his  neighbor  5; 
hpw  many  more  had  he  than  his  neighbor  ? 

3.  A  farmer  had  14  cows,  but  sold  5  of  them  when 
winter  came ;  how  many  had  he  left  ? 

4.  A  ship  had  a  crew  of  13  sailors,  but  5  of  them  de- 
serted ;  how  many  remained  ? 

5.  Frank  had  5  cents,  and  gave  3  cents  for  cake  and  2 
for  candy ;  how  many  had  he  left  ? 

6.  A  hen  came  out  with  a  brood  of  9  chickens,  but 
soon  5  of  them  died ;  how  many  had  she  left  ? 

7.  There  were  7  hooks  on  the  hat-rack,  but  5  of  them 
broke  off ;  how  many  remained  ? 

8.  Robert  had  10  buttons  on  his  coat,  but  5  of  them 
got  pulled  off;  how  many  remained  ? 

9.  Harry  owns  6  chickens,  and  owes  William  5 ;  how 
many  would  Harry  have,  if  he  paid  William  ? 


FOR 

THE    SLATE 

OR   BLACKBOARD. 

8 

11 

14 

13 

5 

9 

7 

10 

6 

11 

5 

5 

5 

5 

5 

5 

5 

5 

6 

5 

34 


SUBTRACTION. 


LESSON   VII. 


6  from  less^ 

impossible. 

6  from     6  leaves  0 

0  from     6  leaves  6 

6  from     7  leaves  1 

1  from     7  leaves  6 

6  from     8  leaves  2 

2  from     8  leaves  6 

6  from     9  leaves  3 

3  from     9  leaves  6 

6  from  10  leaves  4 

4  from  10  leaves  6 

6  from  11  leaves  5 

5  from  11  leaves  6 

6  from  12  leaves  6 

6  from  12  leaves  6 

6  from  13  leaves  7 

7  from  13  leaves  6 

6  from  14  leaves  8 

8  from  14  leaves  6 

6  from  15  leaves  9 

9  from  15  leaves  6 

1.  How  much  more  does  a  pine-apple  cost,  at  12  cents, 
than  an  orange  at  6  cents  ? 

2.  A  boy  earned  10  cents  one  day,  but  spent  6  of  them 
for  food ;  how  many  did  he  clear  ? 

3.  Annie  spelled  6  words  of  her  lesson,  and  Lucy  8 ; 
how  many  more  did  Lucy  spell  than  Annie  ? 

4.  Mary  had  15  cents,  and  spent  all  but  6  of  them ; 
how  many  did  she  spend  ? 

5.  A  boy  put  11  cents  in  his  "  savings-bank-box,^'  and 
then  got  out  6 ;  how  many  remained  ? 

6.  John  had  14  hills  of  corn,  and  the  hens  scratched 
up  all  but  6 ;  how  many  did  they  scratch  up  ? 

7.  If  school  is  kept  9  months  in  the  year,  and  6  are 
gone,  how  long  is  school  yet  to  be  kept  ? 

8.  There  were  7  pins  on  the  cushion,  and  Jane  took  6 
of  them ;  how  many  remained  ? 

9.  There  were  13  pupils  in  the  spelling-class,  and  6  of 
them  were  girls ;  how  many  were  boys  ? 


FOR 

THE    SLATE    OR 

BLACKBOARD. 

12 

10 

8 

15 

11 

14 

9 

7 

13 

6 

6 

_ 

6 

6 

6 

6 

6 

6 

6 

6 

6 

SUBTRACTION. 


85 


LESSON   VIII. 


7  from  lesS; 

impossible. 

7  from     7  leaves  0 

0  from     7  leaves  7 

7  from     8  leaves  1 

1  from     8  leaves  7 

7  from     9  leaves  2 

2  from     9  leaves  7 

7  from  10  leaves  3 

3  from  10  leaves  7 

7  from  11  leaves  4 

4  from  11  leaves  7 

7  from  12  leaves  5 

5  from  12  leaves  7 

7  from  13  leaves  6 

6  from  13  leaves  7 

7  from  14  leaves  7 

7  from  14  leaves  7 

7  from  15  leaves  8 

8  from  15  leaves  7 

7  from  16  leaves  9 

9  from  16  leaves  7 

1.  I  started  to  ride  10  miles,  but,  after  going  7,  my 
carriage  broke  down ;  how  far  had  I  yet  to  go  ? 

2.  I  ordered  12  loads  of  coal;  after  7  had  been  de- 
livered, how  many  were  yet  to  come  ? 

3.  A  merchant  bought  14  barrels  of  molasses ;  after 
he  had  sold  7  of  them,  how  many  remained  ? 

4.  He  bought  16  pounds  of  spice;  after  he  had  sold 
7  pounds  of  it,  how  many  remained  ? 

5.  Thirteen  boys  chose  sides  at  ball ;  after  7  had  been 
chosen,  how  many  were  to  be  chosen  ? 

6.  One  side  got  8  runs,  and  the  other  got  7;   how 
many  more  did  one  side  get  than  the  other  ? 

7.  Eleven  boys  chose  a  captain;  after  7  had  voted, 
how  many  were  yet  to  vote  ? 

8.  James  got  15  blocks  at  the  carpenter's,  and  Helen 
7 ;  how  many  more  did  James  get  than  Helen  ? 

9.  From  a  9-gallon  keg  of  syrup,  I  drew  1,  2,  1,  and 
3  gallons ;  how  much  remained  ? 


FOB 

THE   SLATE   OR 

BLACKBOARD. 

10 

12 

14 

16 

13 

8 

11 

15 

9 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

36 


SUBTRACTION. 


LESSON  IX. 


8  from  lesSj 

impossible. 

from     8  leaves  0 

0  from     8  leaves  8 

from     9  leaves  1 

1  from     9  leaves  8 

f>om  10  leaves  2 

2  from  10  leaves  8 

from  11  leaves  3 

3  from  11  leaves  8 

from  12  leaves  4 

4  from  12  leaves  8 

from  13  leaves  5 

5  from  13  leaves  8 

from  14  leaves  6 

6  from  14  leaves  8 

from  15  leaves  7 

7  from  15  leaves  8 

from  16  leaves  8 

8  from  16  leaves  8 

from  17  leaves  9 

9  from  17  leaves  8 

1.  If  school  has  12  weeks*  vacation  in  a  year,  and  one 
vacation  is  8  weeks,  how  long  is  the  other  ? 

2.  The  parlor  has  15  yards  of  carpet,  the  chamber  8 ; 
how  many  more  has  one  than  the  other  ? 

3.  Mary's  mother  baked  9  •  loaves  and  8  pies ;    how 
many  more  loaves  than  pies  did  she  bake  ? 

4.  Susan  bought  16  sheets  of  paper;  after  she  had 
used  8,  how  many  had  she  left  ? 

5.  John  traded  with  8  cents  till  he  had  1 7  cents ;  how 
many  cents  did  he  make  by  trading  ? 

6.  Alfred  gave  8  cents  for  a  sled,  and  sold  it  for  8 
cents ;  how  much  did  he  make  ? 

7.  George  bought  a  knife  for  14  cents,  and  sold  it 
for  8  cents ;  how  much  did  he  lose  ? 

8.  Charles  bought  a  ball  for  10  cents,  and  sold  it  for 
8  cents ;  how  much  did  he  lose  ? 

9.  If  you  begin  business  with  8  cents,  and  leave  off 
with  13  cents,  how  much  do  you  make  ? 


SUBTRACTION.                                           37 

LESSON  X. 

9  from  less^ 

impossible. 

9  from    9  leaves  0 

0  from     9  leaves  9 

9  from  10  leaves  1 

1  from  10  leaves  9 

9  from  11  leaves  2 

2  from  11  leaves  9 

9  from  12  leaves  3 

3  from  12  leaves  9 

9  from  13  leaves  4 

4  from  13  leaves  9 

9  from  14  leaves  5 

5  from  14  leaves  9 

9  from  15  leaves  6 

6  from  15  leaves  9 

9  from  16  leaves  7 

7  from  16  leaves  9 

9  from  17  leaves  8 

8  from  17  leaves  9 

9  from  18  leaves  9 

9  from  18  leaves  9 

1.  There  was  a  row  of  10  cars,  and  the  engine  took 
away  9  of  them ;  how  many  were  lefl  ? 

2.  If  you  trade  a  sled  at  15  cents,  for  a  ball  at  9  cents, 
and  money,  how  much  money  must  you  get  ? 

3.  There  were  12  panes   in  a  window,  and  the  hail 
broke  9  ;  how  many  remained  whole  ? 

4.  Edward  set  a  trap  and  caught  9  out  of  a  flock  of  17 
pigeons ;  how  many  escaped  ? 

5.  Anna  had  14  beads,  but  the  string  broke  and  she 
lost  all  but  9  }  how  many  did  she  lose  ? 

6.  There  were  11  gas-lights  in  the  street,  but  the  wind 
blew  out  9  ;  how  many  kept  burning  ? 

7.  A  fleet  of  16  vessels  went  to  sea,  but  a  storm  de- 
stroyed all  but  9  'j  how  many  were  lost  ? 

8.  One  of  them  had  18  persons  on  board,  but  only  9 
reached  shore ;  how  many  were  lost  ? 

9.  Another  had  13  persons  on  board,  and  9  were  lost; 
how  many  reached  land  ? 


FOR 

THE    SLATE 

OR   BLACKBOARD. 

10 

15 

12 

17 

14 

11 

16 

18 

13 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

38 


SUBTRACTION. 


LESSON    XL 


10  from  less 

,  impossible. 

10  from  10  leaves  0 

0  from  10  leaves  10 

10  from  11  leaves  1 

1  from  11  leaves  10 

10  from  12  leaves  2 

2  from  12  leaves  10 

10  from  13  leaves  3 

3  from  13  leaves  10 

10  from  14  leaves  4 

4  from  14  leaves  10 

10  from  15  leaves  5 

5  from  15  leaves  10 

10  from  16  leaves  6 

6  from  16  leaves  10 

10  from  17  leaves  7 

7  from  17  leaves  10 

10  from  18  leaves  8 

8  from  18  leaves  10 

10  from  19  leaves  9 

9  from  19  leaves  10 

1.  A  merchant  sold  at  10  cents,  muslin  marked  12 
cents  a  yard ;  how  much  reduction  did  he  make  ? 

2.  Of  14  officers,  only  10  answered  at  roll-call  after  a 
battle;  how  many  were  missing  ? 

3    A  farmer  had  19  sheep,  and  the  dogs  killed  all  but 
10  of  them;  how  many  did  they  kill  ? 

4.  He  had  18  chickens,  and  a  fox  killed  10  of  them; 
how  many  chickens  had  the  farmer  then  ? 

5.  A  owes  B  16  dollars,  and  B  owes  A  10  dollars;  how 
much  must  A  pay  to  B  when  they  settle  ? 

6.  At  another  time  B  owed  17  dollars  to  A,  and  A  10 
dollars  to  B ;  which  must  pay,  and  how  much  ? 

7.  If  C  owes  D  11  dollars,  and  D  owes  C  10  dollars, 
which  pays,  at  settlement,  and  how  much  ? 

8.  If  you  owed  15  cents,  and  paid  10  cents,  how  many 
cents  would  you  still  owe? 

9.  If  you  had  13  cents,  and  owed  10  cents,  how  many 
cents  would  you  have  clear  of  debt  ? 


FOR 

THE 

SLATE 

OR    BLACKBOARD. 

12 

14 

19 

18 

16 

17 

11 

15 

13 

10 

10 

10 

10 

10 

10 

10 

10 

10 

10 

10 

SUBTRACTION.  39 


LESSON    XII. 


REVIEW. 

1. 

6  from  12  leaves  how  many  ? 

7  from  12? 

2. 

5  from  12  ? 

8  from  15  ? 

9  from  10  ? 

3. 

7  from  15  ? 

10  from  15  ? 

5  from    9  ? 

4. 

8  from  12  ? 

4  from    9  ? 

4  from  12  ? 

5. 

7  from  11  ? 

3  from    7  ? 

4  from  11  ? 

6. 

4  from    7  ? 

9  from  18  ? 

2  from  11  ? 

7. 

6  from  15  ? 

5  from  14  ? 

4  from    7  ? 

8. 

5  from    8  ? 

6  from    9? 

7  from  10  ? 

9. 

3  from    8  ? 

8  from  13  ? 

9  from  15  ? 

10. 

2  from    8  ? 

2  from  10  ? 

10  from  18  ? 

11. 

8  from  10  ? 

8  from  16  ? 

10  from  13? 

12. 

9  from  12  ? 

8  from  11  ? 

3  from    6  ? 

13. 

1  from    3  ? 

4  from    6  ? 

6  from    8  ? 

14. 

10  from  12  ? 

7  from  13  ? 

8  from  13  ? 

15. 

9  from  13  ? 

6  from  13  ? 

5  from  13  ? 

16. 

4  from  13  ? 

3  from  13  ? 

6  from  11  ? 

17. 

5  from  11  ? 

9  from  11? 

3  from  11  ? 

18. 

3  from  10  ? 

4  from  10? 

5  from  10  ? 

19. 

6  from  10  ? 

3  from    9? 

7  from    9  ? 

20. 

9  from    9  ? 

8  from    8? 

7  from    7? 

21. 

6  from    6  ? 

5  from    5? 

4  from    4? 

22. 

3  from    3  ? 

2  from    2? 

1  from    1  ? 

23.  If  only  7  apples  were  in  a  basket,  could  you  get  8 
apples  out  of  it  ?    Why  ? 

24.  If  you  take  8  from  14,  the  difference  is  the  same 
as  if  you  took  .5  from  what  ?     Ten  from  what  ? 

25.  From  what  must  you  take  9,  to  have  the  same 
difference  as  6  from  14  gives  ? 

26.  From  what  must  you  take  8,  to  have  the  same 
difference  as  9  from  18  gives  ? 

27.  From  what  must  you  take  9,  to  have  the  same 
difference  as  10  from  17  gives  ?    Seven  from  14  ? 

28    Nine  from  14  leaves  how  many  ?     Ten  from  19  ? 
29.  Two  and  3  are  the  same  as  4  from  what? 


^ g 

40  SUBTRACTION. 


LESSON    XIII. 

PROMISCUOUS    EXERCISES. 

1.  If  you  have  10  cents,  and  give  3  for  an  orange,  and 
2  for  a  lenion,  how  many  cents  have  you  left? 

2.  Jane  had  15  cents,  and  gave  6  for  needles,  and  3 
for  thread ;  how  many  cents  had  she  left  ? 

3.  John  earned  8  cents  one  day,  and  10  cents  the  next 
day;  he  then  spent  7  cents  for  paper,  and  5  cents  for 
pens ;  how  many  cents  had  he  left '/ 

4.  Four  birds  alighted  on  a  tree,  then  7  more;  then  3 
flew  off,  followed  by  5 ;  how  many  remained  ? 

5.  There  were  6  boys  and  7  girls  in  a  party;  when  3 
boys  had  left,  each  with  a  girl,  how  many  persons  re- 
mained ? 

6.  If  you  buy  12  sheets  of  paper,  how  many  have  you 
loft  after  using  9  of  them  ? 

7.  If  there  are  16  pupils  in  a  school,  and  5  boys  and 
4  girls  are  called  out  to  spell,  how  many  pupils  stay  in 

/  their  seats  ? 

8.  There  were  8  houses  on  one  side  of  a  certain  street, 
and  6  on  the  other;  after  a  fire,  4  were  left  on  one  side, 
and  3  on  the  other;  how  many  were  burned  ? 

9.  A  shoemaker  had  8  pairs  of  boots,  and  9  pairs  of 
shoes ;  he  sold  all  the  shoes,  and  3  pairs  of  boots ;  how 
many  pairs  had  he  left  ? 

10.  If  you  have  only  a  ten-cent-piece  and  a  five-cent- 
piece,  can  you  buy  and  pay  for  a  thing  which  costs  20. 
cents  ?    Why  ? 

11.  If  you  had  18  cents,  and  paid  6  cents  for  fare  in 
a  car,  and  5  cents  for  cake,  how  many  cents  would  you 
have  left  ? 

12.  If  you  had  15  cents,  and  spent  9  cents  at  one 
time,  and  6  at  another,  how  many  would  you  have  ? 

13.  If  you  earn  20  cents,  and  spend  15,  are  you  richer 
than  le  who  earns  10  cents  and  spends  5? 

14.  Seven  and  2  are  the  same  as  3  from  what  ? 


iS — 

SUBTRACTION. 

S9 

41 

LESSON    XIV. 

Carry  out  each  followinor  line  as  indicated. 

1. 

How  many  are  1  from  10  ? 

1  from  20? 

lfrom30?&c. 

2. 

2  from  10? 

2  from  20? 

2  from  30? 

2from40?&c. 

3. 

3  from  10? 

3  from  20? 

3  from  30  ? 

3from40?&c. 

4. 

4  from  10? 

4  from  20  ? 

4  from  30? 

4  from  40  ?  &c. 

6. 

5  from  10? 

5  from  20? 

5  from  30? 

5from40?&c. 

6. 

6  from  1^? 

6  from  20  ? 

6  from  30? 

6from40?&c. 

7. 

7  from  10? 

7  from  20? 

7  from  30  ? 

7from40?&c. 

8. 

8  from  10? 

8  from  20? 

8  from  30? 

8from40?&c. 

9. 

9  from  10? 

9  from  20? 

9  from  30  ? 

9from40?&c. 

10. 

2  from  11  ? 

2  from  21  ? 

2  from  31? 

2from41?&c. 

11. 

3  from  11? 

3  from  21? 

3  from  31? 

3  from41?&c. 

12. 

4  from  11? 

4  from  21  ? 

4  from  31? 

4from41?&c. 

13. 

5  from  11? 

5  from  21? 

5  from  31? 

5  from  41  ?  &c. 

14. 

6  from  11? 

6  from  21? 

6  from  31  ? 

6  from  41  ?  &c. 

15. 

7  from  11  ? 

7  from  21? 

7  from  31? 

7from41?&c. 

16. 

2  from    2? 

2  from  12? 

2  from  22? 

2from32?&c. 

17. 

3  from  12? 

3  from  22? 

3  from  32? 

3from42?&c. 

18. 

4  from  12? 

4  from  22  ? 

4  from  32  ? 

4from42?&c. 

19. 

5  from  12? 

5  from  22? 

5  from  32? 

5from42?&c. 

20. 

6  from  12? 

6  from  22? 

6  from  32  ? 

6from42?&c. 

21. 

8  from  12? 

8  from  22? 

8  from  32? 

8from42?&c. 

22. 

3  from    3? 

3  from  13  ? 

3  from  23  ? 

3from33?&c. 

23. 

4  from  13? 

4  from  23? 

4  from  33? 

4from43?&c. 

24. 

5  from  13? 

5  from  23? 

5  from  33? 

5from43?&c. 

25. 

6  from  13  ? 

6  from  23? 

6  from  33  ? 

6from43?&c. 

26. 

7  from  13? 

7  from  23? 

7  from  33  ? 

7from43?&c. 

27. 

8  from  13? 

8  from  23? 

8  from  33? 

8from43?&c. 

28. 

9  from  13? 

9  from  23  ? 

9  from  33  ? 

9from43?&o. 

29. 

2  from    4? 

2  from  14? 

2  from  24? 

2from34?&c. 

30. 

3  from    4? 

3  from  14? 

3  from  24? 

3from34?&c. 

31. 

4  from    4  ? 

4  from  14? 

4  from  24? 

4from34?&c. 

32. 

5  from  14  ? 

5  from  24? 

5  from  34? 

5from44?&c. 

33. 

6  from  14? 

6  from  24? 

6  from  34? 

6from44?&a 

34. 

7  from  14? 

7  from  24? 

7  from  34? 

7from44?&c. 

35. 

g 

8  from  14? 

8  from  24? 

8  from  34? 

8from44?&c. 

4* 


42  SUBTRACTION. 


LESSON    XV. 

1.  How  many  are  2  from  5  ?    2  from  15  ?  &c. 

2.  3  from    5?    S  from  15?    3  from  25?    3  from  35?, tc. 

3.  4  from    5?   4  from  15?   4  from  25?   4from35?&j. 

4.  5  from    5  ?    5  from  15  ?    5  from  25  ?    5  from  35  ?  &c. 

5.  6  from  15?    6  from  25?    6  from  35?    6from45?&c. 

6.  7  from  15?    7  from  25?    7  from  35?    7from45?&c. 

7.  8  from  15?    8  from  25?    8  from  35?    8from45?&c. 

8.  3  from    6?   3  from  16?   3  from  26?   3from36?&c. 

9.  4  from    6?   4  from  16?   4  from  26?   4from36?&c. 

10.  5  from    6?    5  from  16?   5  from  26?   5from36?&c. 

11.  6  from    6?    6  from  16?   6  from  26?    6from36?&c. 

12.  7  from  16?    7  from  26?    7  from  36?    7from46?&c. 

13.  8  from  16?    8  from  26?    8  from  36?   8from46?&c. 

14.  2  from    7?   2  from  17?   2  from  27?   2from37?&c. 

15.  3  from    7?    3  from  17?    3  from  27?    3from,37?&c. 

16.  4  from    7?   4  from  17?   4  from  27?   4from37?&c. 

17.  5  from    7?    5  from  17?    5  from  27?    5from37?&c. 

18.  6  from    7?    6  from  17?    6  from  27?    6from37?&c. 

19.  7  from    7?    7  from  17?    7  from  27?    7from37?&c. 

20.  8  from  17?    8  from  27?    8  from  37?    8from47?&c. 

21.  2  from    8?    2  from  18?    2  from  28?    2from38?&c. 

22.  3  from    8?    3  from  18?    3  from  28?    3from38?&c. 

23.  4  from    8?   4  from  18?   4  from  28?    4from38?&c. 

24.  5  from    8?    5  from  18  ?    5  from  28?    5from38?&c. 

25.  6  from    8?    6  from  18?    6  from  28?    6from38?&c. 

26.  7  from    8?*^7froml8?    7  from  28?    7from38?&c. 

27.  8  from    8?    8  from  18?    8  from  28?   8from38?&c. 

28.  9  from  18?    9  from  28?    9  from  38?  9from48?&c. 

29.  2  from    9?    2  from  19?    2  from  29?   2from39?&c. 

30.  3  from    9?    3  from  19?    3  from  29?   ^from39?&c. 

31.  4  from    9?   4  from  19?   4  from  29?    4from39?&c. 

32.  5  from    9?    5  from  19?   5  from  29?    5from39?&c. 

33.  6  from    9?    6  from  19?    6  from  29?    6from39?&c. 

34.  7  from    9?    7  from  19?    7  from  29?    7from39?&c. 

35.  8  from    9?    8  from  19?    8  from  29?    8from39?&c. 

36.  9  from    9?    9  from  19?    9  from  29?    9from39?&c. 


SUBTRACTION.  43 


LESSON    XVI. 


COUNTING  DOWNWARD. 


Courting  downward  is  a  process  of  subtraction.  If 
you  begin  at  20,  and  count  thus, — 20,  19,  18,  &c., — ^you 
mean  that,  by  taking  1  from  20,  19  are  left;  and  1  from 
19  leaves  18,  &c.  You  can  find,  in  this  way,  the  number 
of  a  thing  in  its  order  in  a  certain  collection  of  things. 
Thus,  you  can  say,  in  counting  20  things  dow^awards, 
20th,  19th,  18th,  &c.,  as  though  they  had  first  been 
counted  and  numbered  the  other  way. 

Now  make  twenty  marks  upon  the  slate  or  blackboard, 
and  count  them  downward,  after  first  counting  them 
upward. 

Now  separate  the  twenty  marks  into  twos  with  commas; 
thus — 

I  \\\  M  \,\  \,\  \,\  \,\  \,\  \,\  \,\  I 

Count  this  row  by  twosj  saying  two,  four,  &c.,  up  to 
twenty.  Then  begin  at  twenty^  and  count  downward  by 
twos. 

Now  separate  this  row  of  marks  as  follows : — 

I.  I  I.  I  i>  I  i>  I  i>  I  i.  I  I.  I  i>  I  i>  I  i>  I  I 

Count  this  row  from  1,  by  twos,  saying  one,  three,  &c. 
Then  begin  at  twenty-one,  and  count  downward  by  twos. 

When  you  have  learned  to  count  thus  with  20  marks, 
make  a  greater  number  of  them,  and  proceed  in  the  same 
way,  as  far  as  a  hundred. 

Note  to  Teachers. — Make  this  a  blackboard  exercise,  till 
the  pupil  can  readily  count  downward  both  by  ones  and  twos. 
Care  should  be  taken  not  to  press  it  to  high  numbers  at  first. 
When  the  blackboard  exercise  has  become  familiar,  use,  as 
counters,  books,  desks,  persons,  coins,  &c.,  till  the  art  is 
acquired. 


I -^ 

44  MULTIPLICATION. 


MULTIPLICATION. 


LESSON  I. 


If  you  write  the  same  number  two  or  more  times,  you 
are  said  to  repeat  that  number. 

By  multiplication  we  find  the  sum  of  the  repetitions 
of  a  number,  without  adding  them. 

1.  If  you  pay  I  cent  each  time  you  cross  a  bridge,  and 
you  cross  3  times,  how  many  cents  do  you  pay  ? 

Answer       1      ^"®  ^^^^  *^^  °°^  ^^^^  ^^^  ^^^  ^®°'  *^®  three  cents. 

BY  Audition  j        ©  O  ©  ©©© 

Answer  by  Multiplication.  Three;  because  three 
times  I  are  3. 

2.  How  many  gloves  are  there  in  4  pairs  ? 

Si   m   Si    fis 

Ans.  Eight.     Four  times  2  gloves  are  8  gloves. 

3.  Four  times  3  men  are  how  many  men  ? 


p  VJ  In  m  m  I]]  iM  VJ 

1  it  a  n  li  a  it  li 

4.  Three  times  4  men  are  how  many  men  ? 

5.  Four  times  5  balls  are  how  many  balls  ? 

#####      (i)#i)#<i)      #####      #i)^ 

6.  Five  times  4  are  how  many  ? 


7.   Six  times  4  are  how  many  ? 

mm       ##       i)i)       as 


^ 


- 

MULTIPLICATION. 

45 

LESSON  II 

Once 

0  is  0. 

Once 

1 

is 

1 

Once 

IS 

1 

Once 

2 

is 

2 

2  times 

are 

2 

Once 

3 

is 

3 

3  times 

are 

8 

Once 

4 

is 

4 

4  times 

are 

4 

Once 

5 

is 

5 

5  times 

are 

5 

Once 

6 

is 

6 

6  times 

are 

6 

Once 

7 

is 

7 

7  times 

are 

7 

Once 

8 

is 

8 

8  times 

are 

8 

Once 

9 

is 

9 

9  times 

are 

9 

Once  10 

is 

10 

10  times 

are 

10 

1.  At  1  cent  each,  how  many  cents  do  2  sticks  of' 
candy  cost  ?     Ans.  2  times  1  cent;  that  is,  2  cents. 

2.  At  1  cent  each,  how  many  cents  do  6  sheets  of 
paper  cost  ?     Why  ? 

3.  At  1  dime  a  day,  how  many  dimes  can  John  earn 
in  10  days  ? 

4.  At  1  dollar  a  day,  how  many  dollars  can  a  man  earn 
in  5  days  ? 

5.  If  each  of  7  boys  owns  a  knife,  how  many  knives 
do  they  all  own  ? 

6.  If  a  horse  eats  1  peck  of  oats  a  Jay,  how  many  pecks 
does  he  eat  in  4  days  ? 

7.  If  a  shoemaker  makes  1  pair  of  shoes  a  day,  how 
many  pairs  docs  he  make  in  9  days  ? 

8.  If  a  slate-pencil  costs  1  cent,  how  many  cents  will 
3  slate-pencils  cost? 

9.  If  you  learn  1  arithmetic-lesson  a  day,  how  many 
lessons  would  you  learn  in  8  days  ? 


FOR    THE    SLATE 

OR 

BLACKBOARE 

1 

2 

1 

6 

1 

10 

1 

5 

1 

7 

1 

1 

1 

1 

1 

2 

1 

6 

1 

10 

1 

5 

1 

7 

1 

4 

9 

3 

8 

1 

46 


MULTIPLICATION. 


LESSON   III. 


2  times 

U  are  0. 

2 

times 

1 

are     2 

Once       2  is 

2 

2 

times 

2 

are     4 

2  times  2  are 

4 

2 

times 

3 

are     6 

3  times  2  are 

6 

2 

times 

4 

are     8 

4  times  2  are 

8 

2 

times 

5 

are  10 

6  times  2  are 

10 

2 

times 

6 

are  12 

6  times  2  are 

12 

2 

times 

7 

are  14 

7  times  2  are 

14 

2 

times 

8 

are  16 

8  times  2  are 

16 

2 

times 

9 

are  18 

9  times  2  are 

18 

2 

times 

10 

are  20 

10  times  2  are 

20 

1.  A  boy  went  a-fishing  2  times,  and  caught  none  each 
time ;  how  many  did  he  catch  ? 

2.  At  2  cents  each,  what  cost  2  lemons  ?     3  lemons  ? 

3.  What  cost  2  oranges  at  3  cents  apiece  ? 

4.  What  cost  2  hats  at  4  dollars  apiece  ?     4  caps  at  2 
dollars  apiece  ? 

6.  What  cost  two  pounds  of  sugar  at  8  cents  a  pound  ? 
What  cost  8  pounds  of  flour  at  2  cents  a  pound  ? 

6.  At  10  cents  a  yard,  what  cost  2  yards  of  ribbon  ? 
What  cost  10  yards  of  ribbon  at  2  cents  a  yard  ? 

7.  At  6  cents  a  peck,  what  cost  2  pecks  of  apples? 
6  barrels  of  apples  at  2  dollars  a  barrel  ? 

8.  At  2  dollars  a  day,  how  much  does  a  man  earn  in 
9  days  ?     How  much  in  2  weeks  at  9  dollars  a  week  ? 

9.  What  cost  5  pairs  of  shoes  at  2  dollars  a  pair? 
What  cost  2  pairs  of  boots  at  5  dollars  a  pair  ? 

10.  At  7  miles  an  hour,  how  far  do  you  go  in  2  hours  ? 
How  far  in  7  hours  at  2  miles  an  hour  ? 


&■ 


FOR    THE 

SLATE 

OR    BLACKBOARD, 

0 

2 

2 
2 

2 
3 

3    4    2 
2    2    4 

8    2 
2    8 

10      2    6    2 
2    10    2    6 

2 
9 

9 
2 

2 

5 

7 
2 

HULTIPLIOATION. 


47 


LESSON    IV. 


3  times  0  are  0. 

3  times 

1 

are     3 

Once 

3 

IS 

3 

3  times 

2 

are     6 

2  times 

3 

are 

6 

3  times 

3 

are     9 

3  times 

3 

are 

9 

3  times 

4 

are  12 

4  times 

3 

are 

12 

3  times 

5 

are  15 

5  times 

3 

are 

15 

3  times 

6 

are  18 

6  times 

3 

are 

18 

3  times 

7 

are  21 

7  times 

3 

are 

21 

3  times 

8 

are  24 

8  times 

3 

are 

24 

3  times 

9 

are  27 

9  times 

3 

are 

27 

3  times 

10 

are  30 

10  times 

3 

are 

30 

1.  Mr.  Reed  gave  William  2  cents  three  times,  and 
John  3  cents  twice ;  how  many  did  each  receive  ? 

2.  Harry  went  to  the  barn  3  days  for  eggs,  and  each 
day  found  3;  how  many  in  all  did  he  find  ? 

3.  If  you  put  5  pears  in  each  of  3  plates,  how  many 
are  in  all?     If  3  pears  in  each  of  5  plates? 

4.  In   8  rows  of  marks,  3  in   each  row,  how  many 
marks  are  there?     In  3  rows,  8  in  each  row? 

5.  My  window  has  4  rows  of  panes,  3  in  a  row;  how 
many  panes  has  it  ?     Reckon  them  another  way. 

6.  In  1  week  are  7  days;  how  many  in  3  weeks?     At 
3  meals  a  day,  how  many  do  you  eat  in  a  week? 

7.  My  orchard  has  10  rows  of  trees,  3  in  each  row; 
tell  the  number  of  trees  in  the  orchard. 

8.  Jane  picked  6  bunches  of  cherries,  3  in  each  bunch; 
how  many  cherries  did  she  pick  ? 

9.  What  cost  3  barrels  of  flour  at  9  dollars  a  barrel? 
Nine  yards  of  cloth  at  3  dollars  a  yard  ? 

FOR    THE    SLATE    OR    BLACKBOARD. 

23  3  53833473   3393 
32  3  3  5384337  10  639 


48 


MULTIPLICATION. 


LESSON  V. 

4  times 

0  are  0. 

4  times 

1  are     4 

Once       4  is       4 

4  times 

2  are     8 

2  times  4  are     8 

4  times 

3  are  12 

8  times  4  are  12 

4  times 

4  are  16 

4  times  4  are  16 

4  times 

5  are  20 

5  times  4  are  20 

4  times 

6  are  24 

6  times  4  are  24 

4  times 

7  are  28 

7  times  4  are  28 

4  times 

8  are  32 

8  times  4  are  32 

4  times 

9  are  36 

9  times  4  are  36 

4  times 

10  are  40 

10  times  4  are  40 

1.  What  cost  2  spools  of  thread  at  4  cents  a  spool  ? 
4  loads  of  coal  at  2  dollars  a  load  ? 

2.  A  military  company  made  4  platoons,  8  in  each; 
how  many  men  were  in  the  company  ? 

3.  Do  6  lemons  at  4  cents   each   cost   more  than  4 
oranges  at  6  cents  each  ?     What  do  both  cost  ? 

4.  At  10  cents  a  pound,  what  cost  4  pounds  of  beef? 
10  pounds  of  flour  at  4  cents  a  pound  ? 

5.  There  are  4  quarts  in  a  gallon ;  how  many  quarts 
are  in  5  gallons  ? 

6.  There  are  4  pecks  in  a  bushel ;  how  many  pecks  are 
in  7  bushels? 

7.  If  a  window  has  4  rows  of  panes,  4  panes  in  a 
row,  how  many  panes  has  the  window  ? 

8.  What  cost  4  yards  of  muslin  at  9  cents  a  yard  ?     9 
pencils  at  4  cents  apiece  ? 

9.  There  are  three  feet  in  a  yard ;  how  many  feet  in  4 
yards  ? 

FOR   THE    SLATE    OR    BLACKBOARD. 


4     2     8     4     6     10 
2     4     4     6     4       4 


4     4     4     4     9     4     3 
10     5     7     4     4     9     4 


MULTIPLICATION. 

49 

LESSON  VI. 

5  times 

0  are  0. 

6  times 

1 

are     5 

Once 

5  is 

5 

6  times 

2 

are  10 

2  times 

5  are 

10 

5  times 

3 

are  15 

3  times 

5  are 

15 

5  times 

4 

are  20 

4  times 

5  are 

20 

5  times 

5 

are  25 

5  times 

5  are 

25 

6  times 

6 

are  30 

6  times 

5  are 

30 

5  times 

7 

are  35 

7  times  5  are 

35 

5  times 

8 

are  40 

8  times 

5  are 

40 

5  times 

J 

are  45 

9  times 

5  are 

45 

5  times 

10 

are  50 

10  times 

5  are 

50 

1.  What  cost  two  bottles  of  ink  at  5  cents  each  ?    Five 
sacks  of  wheat  at  2  dollars  each  ? 

2.  What  cost  5  tumblers  at  10  cents  apiece  ?    Ten  hats 
at  5  dollars  apiece  ? 

3.  What  cost  6  pounds  of  soap  at  5  cents  a  pound? 
Five  pounds  of  mutton  at  6  cents  a  pound  ? 

4.  What  is  the  sum  of  a  column  of  five  8's  ?     Of  a 
column  of  eight  5's  ? 

5.  What  are  the  daily  earnings  of  5  men  at  4  dollars 
each  ?     Of  4  men  at  5  dollars  each  ? 

6.  At  9  miles  an  hour,  how  far  will  a  boat  sail  in  5 
hours  ?     At  5  miles  an  hour,  how  far  in  9  hours  ? 

7.  At  3  cents  a  quart,  what  cost  5  quarts  of   salt? 
Three  pounds  of  tallow  at  5  cents  a  pound  ? 

8.  How  many  apples  could  be  put  in  5  plates,  5  being 
put  in  each  plate  ? 

9.  If  five  persons  sit  in  each  pew,  how  many  persons 
would  7  pews  hold  ? 


FOR   THE    SLATE    OR    BLACKBOARD. 

5 

2 

10 

556854595    3 

5 

5 

5 

2 

5 

5 

10    655854595 

3 

5 

7 

?,., 

"~ 

e- 


50 


MULTIPLICATION. 


LESSON    YII. 


6  times 

0  are  0. 

6  times 

1 

are     6 

Once       6  is 

6 

6  times 

2 

are  12 

2  times  6  are 

12 

6  times 

3 

are  18 

3  times  6  are 

18 

6  times 

4 

are  24 

4  times  6  are 

24 

6  times 

5 

are  30 

5  times  6  are 

30 

6  times 

6 

are  36 

6  times  6  are 

36 

6  times 

7 

are  42 

7  times  6  are 

42 

6  times 

8 

are  48 

8  times  6  are 

48 

6  times 

9 

are  54 

9  times  6  are 

54 

6  times  10 

are  60 

10  times  6  uie 

60 

1.  If  each  boy  has  2  hands,  how  many  hands  have  6 
boys  ? 

2.  If  each  girl  has  10  fingers,  how  many  fingers  have 
6  girls? 

3.  If  there  are  6  buttons  on  each  of  6  vests,  how  many 
buttons  are  there  on  all  of  them  ? 

4.  If  one  yard  of  calico  costs  7  cents,  how  much  do  6 
yards  of  the  same  cost  ? 

5.  There  are  8  quarts  in  one  peck;  how  many  are  there 
in  6  pecks  ? 

6.  If  a  family  uses  6  pounds  of  butter  in  a  week,  how 
many  pounds  do  they  use  in  5  weeks  ? 

7.  If  a  cow  gives  6  quarts  of  milk  every  day,  how 
many  quarts  does  she  give  in  9  days  ? 

8.  If  a  horse  eats  6  quarts  of  oats  every  day,  how 
many  quarts  does  he  eat  in  4  days  ? 

9.  If  a  person  pays  6  dollars  a  week  for  board,  how 
much  does  his  board  cost  in  3  weeks  ? 


FOR    THE    SLATE    OR 

BLACKBOARD. 

2 

10 

6        7        8 

6        6 

6 

6 

6 

6 

6        6        6 

5        9 

4 

3 

MULTIPLICATION. 


51 


LESSON    VIII. 


times 
times 
times 
times 
7  times 
7  times 
7  times 
7  times 
7  times 


7  times  0 

7 
14 


times  10 


are 
are 
are  21 
are  28 
are  35 
are  42 
are  49 
are  56 
are  63 
are  70 


are  0. 
Once 
2  times 


times 
times 
times 
times 
times 

8  times 

9  times 
10  times 


is  7 

are  14 

are  21 

are  28 

are  35 

are  42 

are  49 

are  56 

are  63 

are  70 


1.  John's  potato-patcli  had  9  hills  lengthwise,  and  7 
breadthwise ;  how  many  hills  had  it  ? 

2.  His  melon-patch  had  7  hills  in  its  length,  and  4  in 
its  breadth ;  how  many  melon-hills  had  it  ? 

3.  His  patch  of  corn  had  10  hills  in  its  leiigth,  and  7 
in  its  breadth;  how  many  hills  of  corn  had  it  ? 

4.  There  are  8  rows  of  hat-hooks  in  the  hall,  7  in  each 
row;  how  many  hooks  are  there? 

5.  One  side  of  the  house  has  7  windows,  of  6  panes 
each ;  how  many  panes  have  all  the  windows  ? 

6.  The  parlor  carpet  has  5  breadths,  each  7  yards  long; 
how  many  yards  are  in  the  carpet? 

7.  There  are  7  days  in  one  week;  how  many  days  are 
there  in  7  weeks  ? 

8.  Oliver  sold  3  melons,  at  7  cents  apiece;  how  much 
did  he  get  for  them  ? 

9.  The  fare  between  two  cities  is  7  dollars;  what  does 
it  cost  to  ojo  and  return  ? 


FOR 

THB 

SLATE 

OB 

BLACKBOARD. 

9 

7 

4 

7 

10 

7 

8 

7  6  7 

7 

7 

7 

7 

9 

7 

4 

7 

10 

7 

8  7  5 

7 

3 

2 

a 


52 


MULTIPLICATION. 


LESSON    IX. 


8  times 

0  are  0. 

8 

times 

1 

are     8 

Once 

8 

is 

8 

8 

times 

2 

are  16 

2  times 

8 

are 

16 

8 

times 

3 

are  24 

3  times 

8 

are 

24 

8 

times 

4 

are  32 

4  times 

8 

are 

32 

8 

times 

5 

are  40 

5  times 

8 

are 

40 

8 

times 

6 

are  48 

6  times 

8 

are 

48 

8 

times 

7 

are  56 

7  times 

8 

are 

56 

8 

times 

8 

are  64 

8  times 

8 

are 

64 

8 

times 

9 

are  72 

9  times 

8 

are 

72 

8 

times  10 

are  80 

10  times 

8 

are 

80 

1.  At  8   cents  each,  what  cost  6  loaves  of  bread? 
What  cost  8  loaves  at  6  cents  each  ? 

2.  There  ire  8  bones  in  the  wrist;  how  many  are  there 
in  both  wris  s  ? 

3.  One  boy  worked  8  days  at  10  cents  a  day;  another 
10  days  at  8  cents  a  day;  what  did  each  earn  ? 

4.  Kbw  many   gallons  can    five  8-gallon  kegs  hold? 
Eight  5-gallon  kegs  ? 

5.  What  is  the  sum  of  a  column  of  eight  O^s? 

6.  Eight  quarts  make  1  peck ;  how  many  quarts  are 
there  in  4  pecks  ? 

7.  How  many  quarts  are  there  in  8  pecks? 

8.  What  cost  7  yards  of  muslin  at  8  cents  a  yard? 
Eight  yards  of  ribbon  at  7  cen^iJ  a  yard  ? 

9.  If  you  sleep  8  hours  each  day,  how  many  hours  do 
you  sleep  in  3  days  ? 

10.  If  you  study  8  hours  each  day,  how  many  hours 
do  you  study  in  9  days  ? 


FOR   THE    SLATE    OR    BLACKBOARD. 

868  10   8850888788 
682   8  10  588487839 


MULTIPLICATION. 


53 


LESSON    X. 


9  times  0  are  0. 

9  times 

1  are     9 

Once       9  is       9 

9  times 

2  are  18 

2  times  9  are  18 

9  times 

3  are  27 

3  times  9  are  27 

9  times 

4  are  36 

4  times  9  are  36 

9  times 

5  are  45 

5  times  9  are  45 

9  times 

6  are  54 

6  times  9  are  54 

9  times 

7  are  63 

7  times  9  are  63 

9  times 

8  are  72 

8  times  9  are  72 

9  times 

9  are  81 

9  times  9  are  81 

9  times  10  are  90 

10  times  9  are  90 

1.  How  much  more  are  nine  O's  than  eight  O's  ? 

2.  Nine  men  paid  each  9  dollars  stage-fare;  how  many 
dollars  did  all  pay? 

3.  If  a  ferry-boat  makes  9  trips  each  hour,  how  many 
trips  does  it  make  in  10  hours? 

4.  If  an  omnibus  makes  9  trips  a  day,  how  many  trips 
does  it  make  in  6  days  ? 

5.  If  a  man  earns  9  dollars  a  week,  how  many  dollars 
does  he  earn  in  4  weeks  ? 

6.  How  many  pages  have  9  leaves  of  a  book  ? 

7.  In  an  omnibus,  9  girls  paid  each  5  cents  fare;  how 
many  cents  did  all  pay? 

8.  On  the  ferry-boat,  each  paid  3  cents;  how  many 
cents  did  the  boat-trip  cost  them  all  ? 

9.  If  you  read  9  pages  a  day  in  a  book,  how  many 
pages  would  you  read  in  7  days  ? 

10.  At  9  cents  a  dozen,  what  cost  8  dozen  of  eggs? 
What  cost  9  dozen,  at  8  cents  a  dozen  ? 


FOR   THE    SLATE 

OR   BLACKBOARD 

0 

0 

9 

9 

9 

9 

2 

5 

3 

9 

9 

8 

9 

8 

9 

10 

6 

4 

9 

9 

9 

7 

8 

9 

5* 


ffl 


54 


MULTIPLICATION. 


LESSON    XL 


10  times  0  are  0. 

10  times 

1  are 

10 

Once       10  is 

10 

10  times 

2  are 

20 

2  times  10  are 

20 

10  times 

3  are 

30 

3  times  10  are 

30 

10  times 

4  are 

40 

4  times  10  are 

40 

10  times 

5  are 

50 

5  times  10  are 

50 

10  times 

6  are 

60 

6  times  10  are 

60 

10  times 

7  are 

70 

7  times  10  are 

70 

10  times 

8  are 

80 

8  times  10  are 

80 

10  times 

9  are 

90 

9  times  10  are 

90 

10  times  10  are 

100 

10  times  10  are 

100 

1.  How  old  is  a  man  who  has  lived  as  many  years  as  5 
boys,  each  10  years  old  ? 

2.  At  10  cents  apiece,  what  cost  3  copy-books  ?     At  3 
cents  apiece,  what  cost  10  pencils  ? 

3.  How  much  will  7  quarts  of  molasses  cost,  at  10 
cents  a  quart  ? 

4.  How  many  cents  are  9  ten-cent-pieces  worth  ?     At 
9  cents  each,  what  cost  10  spelling-books  ? 

5.  If  each  person  has  10  toes,  how  many  toes  have  10 
persons  ? 

6.  If  a  person  works  10  hours  a  day,  how  many  hours 
does  he  work  in  6  days  ? 

7.  At  10  cents  apiece,  what  cost  2  melons?     At  2 
cents  apiece,  what  cost  10  bunches  of  grapes  ? 

8.  How  many  wheels  have  10  wagons  of  4  wheels 
each? 

9.  How  many  wheels  have  10  railroad  cars  of  8  wheels 
each  ? 


FOR 

THE    SLATE 

OR   BLACKBOARD. 

10 

10 

3 

10 

10 

9 

10 

10 

10 

2 

4 

8 

5 

3 

10 

7 

9 

10 

10 

6 

2 

10 

10 

10 

83 

'HH 

P 

99 

MULTIPLICATION. 

55 

LESSON    XIL 

REVIEW. 

1. 

How  many  are 

4  times    8? 

8  times 

4? 

2. 

2  times 

9? 

6  times   3  ? 

9  times 

2? 

3. 

3  times 

6? 

7  times   5? 

7  times 

10? 

4. 

5  times 

7? 

10  times   7  ? 

9  times 

9? 

5. 

9  times 

7? 

9  times   5? 

9  times 

3? 

6. 

6  times 

2? 

3  times   4? 

2  times 

6? 

7. 

4  times 

3? 

10  times   2? 

4  times 

5? 

8. 

5  times 

4? 

2  times  10  ? 

4  times 

4? 

9. 

2  times 

8? 

8  times   2? 

8  times 

8? 

10. 

6  times 

4? 

8  times   3  ? 

4  times 

6? 

11. 

3  times 

8? 

5  times   3  ? 

3  times 

3? 

12. 

3  times 

6? 

6  times  10? 

2  times 

0? 

13. 

3  times 

0? 

4  times   0? 

6  times 

0? 

14. 

6  times 

0? 

7  times   0  ? 

8  times 

0? 

15. 

9  times 

0? 

10  times   3? 

6  times 

5? 

16. 

5  times 

6? 

4  times    7  ? 

7  times 

4? 

17. 

5  times 

5? 

3  times   7? 

7  times 

2? 

18. 

8  times 

7? 

6  times   9? 

9  times 

6? 

19. 

7  times 

8? 

6  times   8? 

5  times 

10? 

20. 

8  times 

6? 

10  times   5? 

8  times 

5? 

21. 

7  times 

6? 

5  times   8? 

6  times 

7? 

22. 

6  times 

6? 

9  times   4? 

4  times 

9? 

23. 

3  times  10  ? 

Once       2? 

2  times 

1? 

24. 

3  times 

1? 

Once       3? 

Once 

4? 

25. 

4  times 

1? 

Once       5? 

6  times 

1? 

26. 

6  times 

2? 

10  times  10? 

9  times  10?         | 

27. 

10  times 

9? 

9  times   8  ? 

10  times 

8? 

28. 

8  times  10? 

8  times   9  ? 

2  times 

2? 

29. 

3  times 

2? 

2  times   3? 

4  times 

2? 

30. 

2  times 

4? 

10  times   6? 

10  times 

4? 

31. 

4  times  10? 

7  times   9? 

7  times 

7? 

32. 

7  times 

3? 

5  times   9? 

3  times 

9? 

33. 

2  times 

7? 

8  times   4? 

10  times 

0? 

34. 

8  times 

1? 

9  times    1? 

10  times 

1? 

a 

a 

56  MULTIPLICATION. 


LESSON   XIII. 

PROMISCUOUS    EXERCISES. 

1.  If  you  did  not  know  the  Multiplication  Table,  and 
should  buy  6  oranges  at  3  cents  apiece,  how  would  you 
manage  to  know  what  to  pay  ? 

2.  If  you  buy  4  lemons  at  2  cents  apiece,  and  3  cents' 
worth  of  candy,  what  do  you  pay  for  both  ? 

3.  If  you  buy  2  pencils  at  5  cents  apiece,  and  3  pieces 
of  rubber  at  3  cents  apiece,  what  do  you  pay  for  all  ? 
How  much  more  do  you  pay  for  the  one  than  for  the 
other  ? 

4.  If  you  buy  2  spools  of  thread  at  4  cents  apiece,  and 
offer  a  ten-cent-piece,  that  is  a  dime,  what  change  should 
you  receive  ? 

5.  If  you  buy  3  spools  at  4  cents  apiece,  and  offer  a 
dime  and  a  five-cent-piece,  how  much  change  should  you 
receive  ? 

6.  If  you  buy  3  oranges  at  2  cents  apiece,  and  sell  2 
of  them  at  3  cents  apiece,  what  do  you  gain  ? 

7.  If  you  buy  4  pencils  at  4  cents  apiece,  and  sell  3 
of  them  at  5  cents  apiece,  what  does  the  pencil  which 
you  keep  cost  you  ? 

8.  If  you  sell,  at  3  cents  apiece,  3  bottles  of  ink  which 
cost  you  5  cents  apiece,  how  much  do  you  lose  ? 

9.  How  many  more  panes  are  in  a  window  of  5  rows 
and  4  panes  in  a  row,  than  in  a  window  of  6  rows  and  3 
panes  in  a  row  ? 

10.  How  many  less  trees  are  in  an  orchard  of  6  rows 
and  4  trees  in  a  row,  than  in  an  orchard  of  5  rows  and  5 
trees  in  a  row  ? 

11.  If  you  buy  6  balls  at  5  cents  apiece,  and  sell  4  of 
them  at  6  cents  apiece,  and  the  other  2  at  4  cents  apiece, 
how  much  do  you  gain  ? 

12.  How  much  must  be  paid  for  2  pounds  of  sugar  at 
8  cents  a  pound  ? 


&- 


DIVISION. 


57 


DIVISION. 


LESSON  I. 

By  division  we  find  how  many  times  one  number  con- 
tains another. 

1.  How  many  times  1  cent  in  4  cents? 

O  OOOO 

2.  Into  how  many  twos  can  you  arrange  6  balls  ?    Into 
how  many  threes  ? 

Six  balls.  Six  balls. 


3.  Into  how  many  bunches,  of  3  each,  can  you  divide 
nine  cherries  ?  Twelve  cherries  ? 


4.  Into  how  many  groups,  of  4  each,  can  you  divide 
sixteen  marbles  ? 


5.  Into  how  many  heaps,  of  five  each,  can  you  divide  ^ 
twenty  marbles  ? 


6.  Into  how  many  groups,  of  6  each,  can  you  divide 
thirty  balls  ? 

Six  is  contained  in  30  five  times. 


58 

DIVISION. 

LESSON 

11. 

1  in  0  no  time. 

m 

1 

once. 

1 

m 

1  once. 

in 

2 

2 

times. 

2 

m 

2  once. 

in 

3 

3 

times. 

3 

in 

3  once. 

in 

4 

4 

times 

4 

in 

4  once. 

in 

5 

5 

times. 

5 

in 

5  once. 

in 

6 

6 

times. 

6 

in 

6  once. 

in 

7 

7 

times. 

7 

in 

7  once. 

in 

8 

8 

times. 

8 

m 

8  once. 

in 

9 

9 

times. 

9 

in 

9  once. 

in 

10 

10 

times. 

10 

in 

10  once. 

1.  At  1  cent  apiece,  how  many  slate-pencils  can  you 
buy  for  3  cents  ? 

Answer.  As  many  pencils  as  1  cent  is  contained  times 
in  3  cents;  that  is, 3  pencils. 

2.  At  1  dollar  a  bushel,  how  many  bushels  of  rye  can 
you  buy  for  5  dollars  ? 

3.  At  1  dime  a  day,  how  many  days  will  it  take  you  to 
earn  8  dimes  ? 

4.  At  one  bucketful  a  minute,  how  many  minutes  will 
it  take  you  to  draw  10  bucketfuls  of  water  ? 

5.  If  a  man  makes  1  pair  of  shoes  in  a  day,  how  many 
days  will  he  be  in  making  6  pairs  ? 

6.  If  a  horse  eats  1  peck  of  oats  a  day,  in  how  many 
days  will  he  eat  4  pecks  ? 

7.  At  1  dollar  wages  a  day,  in  how  many  days  can  a 
man  earn  7  dollars  ? 

8.  If  boarding  is  1  dollar  a  day,  in  how  many  days 
will  it  amount  to  9  dollars  ? 

FOR   THE    SLATE    OR    BLACKBOARD. 

1)3    1)5    1)8    1)10    1)6    1)4    1)7    1)9 


DIVISION. 


59 


LESSON  III. 


2  in  less 

no  time 

2 

in     2 

once. 

1 

m 

2  2  times. 

2 

in     4 

2  times. 

2  ] 

m 

4  2  times 

2 

in     6 

3  times. 

3 

in 

6  2  times 

2 

in     8 

4  times. 

4 

m 

8  2  times 

2 

in  10 

5  times. 

5 

m 

10  2  times. 

2 

in  12 

6  times. 

6 

m 

12  2  times. 

2 

in  14 

7  times. 

7  ] 

in 

14  2  times. 

2 

in  16 

8  times. 

8  ] 

in 

16  2  times. 

2 

in  18 

9  times. 

9  ] 

in 

18  2  times. 

2 

in  20 

10  times. 

10  ] 

in 

20  2  times. 

1.  If  2  lemons  cost  4  cents,  what  does  1  cost  ? 

2.  If  2  oranges  cost  6  cents,  what  does  1  cost  ? 

3.  If  2  hats  cost  8  dollars,  what  does  1  hat  cost?  If 
4  caps  cost  8  dollars,  what  does  1  cap  cost  ? 

4.  If  2  pounds  of  sugar  cost  16  cents,  what  costs  1 
pound?  If  8  pounds  of  flour  cost  16  cents,  what  does 
1  pound  cost? 

5.  If  a  man  earns  18  dollars  in  2  weeks,  how  much  is 
that  a  week  ? 

6.  If  2  pecks  of  apples  cost  12  cents,  what  does  1  peck 
cost?  If  6  barrels  of  apples  cost  12  dollars,  what  does 
1  barrel  cost? 

7.  If  2  yards  of  ribbon  cost  20  cents,  how  much  is 
that  a  yard  ? 

8.  If  2  pairs  of  boots  cost  10  dollars,  how  much  is 
that  a  pair  ? 

9.  If  a  horse  walks  steadily  4  miles  in  2  hours,  how 
far  is  that  an  hour?  If  a  man  walks  steadily  14  miles 
in  7  hours,  how  far  is  that  an  hour  ? 


FOR    THE    SLATE    OR    BLACKBOARD. 

2)4     2)6    2)8     4)8     2)16     8)16     2)18     2)12 


60 


DIVISION. 


LESSON  lY. 


m  3 
in  6 
in  9 
n  12 
n  15 
n  18 
21 
24 
n  27 


3  in  less 
once. 

2  times. 

3  times. 

4  times. 

5  times. 

6  times. 

7  times. 

8  times. 

9  times. 


no  time. 


n  30  10  times. 


in  9 
in  12 
in  15 
in  18 
in  21 

8  in  24 

9  in  27 
10  in  30 


times, 
times, 
times, 
times, 
times, 
times, 
times, 
times, 
times, 
times. 


1.  If  you  receive  6  cents  in  3-cent-pieces,  how  many- 
do  you  receive  ?  If  in  2-cent  gifts,  how  many  gifts  do 
you  receive  ? 

2.  If  Harry  finds  3  eggs  a  day,  in  how  many  days  does 
he  find  9  eggs  ? 

3.  If  15  pears  are  put  into  plates,  3  in  each  plate,  how 
many  plates  are  used?  How  many  if  5  are  put  in  a 
plate  ? 

4.  How  many  bunches  would  24  cherries  make,  3  in  a 
bunch  ?     How  many,  8  in  a  bunch  ? 

5.  If  a  window  has  12  panes  of  glass,  3  in  a  row,  how 
many  rows  of  panes  has  the  window  ? 

6.  If  you  eat  3  meals  a  day,  in  how  many  days  will 
you  eat  21  meals? 

7.  An  orchard  has  30  trees  in  rows  of  3  trees  each ; 
how  many  such  rows  has  the  orchard  ? 

8.  At  3  dollars  a  barrel,  how  many  barrels  of  flour 
will  18  dollars  buy  ?  If  27  dollars  buy  3  barrels  of  flour, 
what  is  the  price  ? 

FOR    THE    SLATE    OR    BLACKBOARD. 

^3)6    3)9     3)15     3)24     3)12     3)21     3)30    3)18 


DIVISION 


61 


LESSON  V. 


4  in 

4 

4 


m  4 
in  8 
in  12 
in  16 

20 


in  24 

in  28 


in  32 
in  36 
in  40  10 


4  in  less 
once, 
times, 
times, 
times, 
times, 
times, 
times, 
times, 
times, 
times. 


no  time. 
1  in 


2  in 

3  in  12 

4  in  16 

5  in  20 

6  in  24 

7  in  28 

8  in  32 

9  in  36 
10  in  40 


8  4  ti 


mes. 
mes. 
mes. 
mes. 
mes. 
mes. 
mes. 
mes. 
mes. 
mes. 


—■      1.  If  4  cents  buy  1  spool  of  thread,  how  many  spools 
will  8  cents  buy  ? 

2.  How  many  platoons,  of  8  men  each,  can  a  company 
of  32  men  form  ? 

3.  How  many  quarts  of  salt,  at  4  cents  a  quart,  can 
you  buy  for  24  cents  ? 

4.  How  many  pounds  of  flour,  at  4  cents  a  pound,  can 
you  buy  for  40  cents  ? 

5.  A  gallon  contains  4  quarts ;  how  many  gallons  are 
there  in  20  quarts  ? 

6.  A  bushel  contains  4  pecks ;  how  many  bushels  are 
there  in  28  pecks  ? 

7.  If  16  cents  are  divided  equally  among  4  boys,  how 
many  cents  does  each  boy  receive  ? 

8.  At  9  cents  a  yard,  how  many  yards  of  muslin  can 
you  buy  for  36  cents  ?  How  many  pencils,  at  4  cents 
apiece,  can  you  buy  for  36  cents  ? 

9.  How  many  hats,  at  4  dollars  apiece,  can  you  buy 
for  12  dollars  ? 

FOR   THE    SLATE    OR    BLACKBOARD. 

4)8  8)32  4)24  4)40  4)20  4)28  4)16  4)36  4)12 

e : 8 


62 


DIVISION. 


-m 


LESSON    VL 


5  in  less 

no  time. 

5  in    5 

once. 

lin    5 

5  times 

5  in  10 

2  times. 

2  in  10 

5  times. 

5  in  15 

3  times. 

Sin  15 

5  times 

5  in  20 

4  times. 

4  in  20 

5  times 

5  in  25 

5  times. 

5  in  25 

5  times 

5  in  30 

6  times. 

6  in  30 

5  times 

5  in  35 

7  times. 

7  in  35 

5  times 

5  in  40 

8  times. 

8  in  40 

5  times 

5  in  45 

9  times. 

9  in  45 

5  times 

5  in  50 

10  times. 

10  in  50 

5  times 

1.  If  5  persons  sit  in  each  pew,  how  many  pews  would 
35  persons  occupy? 

2.  If  5  boys  sit  on  each  bench,  how  many  benches 
would  be  needed  for  25  boys  ? 

3.  How  many  pounds  of  tallow,  at  5  cents  a  pound, 
can  be  bought  for  15  cents? 

4.  If  a  boat  sails  5  miles  an  hour,  how  many  hours 
will  it  be  in  sailing  45  miles  ? 

5.  If  5  men  receive  equal  wages  and  earn  20  dollars 
a  day,  what  does  each  man  receive? 

6.  How  many  5's  must  you  write  in  a  column  to  make 
the  sum  of  the  column  equal  40  ? 

7.  How  many  pounds  of  soap,  at  5  cents  a  pound,  can 
you  buy  for  30  cents? 

8.  How  many  hats,  at  5  dollars  apiece,  can  you  buy 
for  50  dollars  ? 

9.  If  5  sacks  of  wheat  cost  10  dollars,  what  does  1 
sack  cost  ?  If  2  bottles  of  ink  cost  10  cents,  what  does 
1  bottle  cost  ? 


FOR    THE    SLATE    OR    BLACKBOARD. 

5)35     5)25     5)15     5)45     5)20    5)40    5)30    5)50 


r- 


r. 


DIVISION. 


63 


LESSON    VIL 


n  6 
nl2 

nl8 
n24 
n30 
n36 
n42 
n48 
n54 
n60 


6  in 
once. 

2  times. 

3  times. 

4  times. 

5  times. 

6  times. 

7  times. 

8  times. 

9  times. 
10  times. 


less  no  time. 


m  6 
in  12 
in  18 
in  24 
in  30 
in  36 
in  42 

8  in  48 

9  in  54 
10  in  60 


1 
2 

3 
4 
5 
6 

7 


times. 

times. 

times. 

times. 

times. 

times. 
6  times. 
6  times. 
6  times. 
6  times. 


1.  If  each  boy  has  2  hands,  how  many  boys  will  it 
take  to  show  12  hands  ? 

2.  If  each  girl  has  10  fingers,  how  many  girls  must 
there  be  to  have  60  fingers  ? 

3.  How  many  vests  will  36  buttons  supply,  if  each  vest 
has  6  buttons  ? 

4.  At  6  cents  a  yard,  how  many  yards  of  calico  can  be 
bought  for  42  cents  ?     At  7  cents  a  yard  ? 

5.  If  you  divide  48  quarts  into  6  equal  measures,  how 
many  quarts  will  be  in  each  measure?  If  into  peck 
measures,  of  8  quarts  each,  how  many  will  there  be  ? 

6.  If  a  family  eats  6  pounds  of  butter  in  a  week,  in 
how  many  weeks  would  it  eat  30  pounds  ? 

7.  If  a  cow  gives  6  quarts  of  milk  a  day,  in  how  many 
days  will  she  give  54  quarts  ? 

8.  If  a  horse  eats  6  quarts  of  oats  in  a  day,  in  tow 
many  days  will  he  eat  24  quarts  ? 

9.  If  boarding  is  6  dollars  a  week,  for  how  many  wecks^ 
boarding  will  18  dollars  pay? 


FOR   THE    SLATE    OR    BLACKBOARD. 

2)12    10)60    6)36    6)42    6)48     8)48     6)30    6)54 


64 


DIVISION 


LESSON    VIIL 


14 
21 

28 
35 
42 
49 
56 
63 
70 


Tin 
once. 

2  times. 

3  times. 

4  times. 

5  times. 

6  times. 

7  times. 

8  times. 

9  times. 
10  times. 


less 


no  time. 


1  in    7 

7  times 

2  in  14 

7  times 

3  in  21 

7  times 

4  in  28 

7  times 

5  in  35 

7  times 

6  in  42 

7  times 

7  in  49 

7  times 

8  in  56 

7  times 

9  in  63 

7  times 

Oin70 

7  times. 

1.  Seven  days  make  a  week;  how  many  weeks  are 
there  in  63  days  ? 

2.  How  many  weeks  are  there  in  28  days  ? 

3.  If  you  saved  7  dollars  a  week,  in  how  many  weeks 
would  you  save  70  dollars  ? 

4.  If  a  horse  trots  7  miles  each  hour,  in  how  many 
hours  would  he  trot  21  miles  ? 

5.  In  the  hall  there  are  56  hat-hooks,  in  7  equal  rows; 
how  many  hooks  are  there  in  each  row  ? 

6.  If  7  equal  windows  have  42  panes,  how  many  panes 
are  there  in  each  window? 

7.  If  a  carpet  has  7  equal  breadths,  and  is  made  of  35 
yards  of  carpeting,  how  many  yards  of  carpeting  are  there 
in  each  breadth  ? 

8.  If  melons  are  7  cents  apiece,  how  many  can  you 
buy  for  14  cents  ? 

9.  If  the  fare  on  a  railroad  between  two  cities  is  7 
dollars,  how  many  persons  can  go  from  one  city  to  the 
other  for  49  dollars  ? 

FOR    THE    SLATE    OR   BLACKBOARD. 

7)63   7)28   7)70  7)21  7)56  7)42  7)35  7)14  7)49 


DIVISION. 


65 


n  » 
nl6 
ii24 
ii32 
ii40 
n48 
n56 
ii64 
n72 
n80 


LESSON    IX. 

8  in  less  no  time 


m 
once. 

2  times. 

3  times. 

4  times. 

5  times. 

6  times. 

7  times. 

8  times. 

9  times. 
10  times. 


lin    8 

8  times. 

2  in  16 

8  times. 

3  in  24 

8  times. 

4  in  32 

8  times. 

5  in  40 

8  times. 

6  in  48 

8  times. 

7  in  56 

8  times. 

8  in  64 

8  times. 

9  in  72 

8  times. 

10  in  80 

8  times. 

1.  If  a  loaf  of  bread  costs  8  cents,  how  many  sucli 
loaves  can  be  bought  for  48  cents  ? 

2.  If  you  sleep  8  hours  each  day,  in  how  many  days 
do  you  sleep  24  hours  ? 

3.  If  you  read  8  pages  each  day,  in  how  many  days 
would  you  read  80  pages  ? 

4.  If  you  walk  8  miles  each  day,  in  how  many  days 
would  you  walk  40  miles  ? 

5.  Eight  quarts  make  a  peck;  how  many  pecks  are 
there  in  32  quarts  ? 

6.  At  8  cents  a  yard,  how  many  yards  of  calico  can  be 
bought  for  72  cents  ? 

7.  At  8  cents  a  dozen,  how  many  dozen  of  eggs  can  be 
bought  for  64  cents  ? 

8.  If  8  boys  sit  on  each  bench,  how  many  such  benches 
are  needed  for  16  boys  ? 

9.  If  56  gallons  of  cider  are  put  into  kegs,  each  hold- 
ing 8  gallons,  how  many  kegs  does  it  take  ?  If  the  kegs 
hold  7  gallons,  how  many  are  needed  ? 

FOB   THE    SLATE    OR    BLACKBOARD. 

8)48   8)24   8)80  8)40  8)32  8)72  8)64  8)16  8)56 


6* 


66 

DIVISION. 

— & 

LESSON    X. 

9  in  less  no  time. 

9  in    9 

once. 

lin    9 

9  times. 

9  in  18 

2  times. 

2  in  18 

9  times. 

9  in  27 

3  times. 

3  in  27 

9  times. 

9  in  36 

4  times. 

4  in  36 

9  times. 

9  in  45 

5  times. 

5  in  45 

9  times. 

9  in  54 

6  times. 

6  in  54 

9  times. 

9  in  63 

7  times. 

7  in  63 

9  times. 

9  in  72 

8  times. 

8  in  72 

9  times. 

9  in  81 

9  times. 

9  in  81 

9  times. 

9  in  90 

10  times. 

10  in  90 

9  times, 
re,  how  much 

1.  If  9  men  pay  81  dollars  for  stage-fa 

is  that  apiece 

? 

2.  At  9  trips  an  hour,  in  how  many  hours  would  a  | 

ferry-boat  make  90  trips  ? 

3.  At  9  trips  a  day,  in  how  many  day 

s  would  a  car 

make  54  trips 

3? 

4.  If  a  man  earns  9  dollars  a  week,  in  how  many  weeks  | 

would  he  earn  36  dollars  ? 

5.  If  9  girls  were  charged  45  cents  for  a 

L  ride  in  a  car. 

how  much  would  it  be  for  each  ? 

6.  If  each 

day's  work  were  9  hours  long,  how  many 

days'  work  would  there  be  in  27  hours'  work  ? 

7.  At  9  cents  a  day,  how  many  days  would  it  take  you 

to  earn  18  cents  ? 

8.  If  you 

wrote  9  lines  each  day  in  your  copy-book, 

in  how  many 

days  would  you  write  72  lines  ? 

9.   If  each    coach    carries   9    passengers,    how  many 

coaches  would  be  needed  for  63  passengers?     If  each 

coach  carries 

7  passengers? 

FOR    THE    SLATE    OR    BLACKBOARD 

9)81   9)90 

9)54  9)36  9) 

45  9)27  9)18  9)72  9)63 

X 

DIVISION. 

67 

LESSON    XL 

10  in 

less 

J  no  time. 

10  in 

10 

once. 

lin    10 

10  times. 

10  in 

20 

2  times. 

2  in    20 

10  times. 

10  in 

30 

3  times. 

3  in    30 

10  times. 

10  in 

40 

4  times. 

4  in    40 

10  times. 

10  in 

50 

5  times. 

6  in    50 

10  times. 

10  in 

60 

6  times. 

6  in    60 

10  times. 

10  in 

70 

7  times. 

7  in    70 

10  times. 

10  in 

80 

8  times. 

8  in    80 

10  times. 

10  in 

90 

9  times. 

9  in    90 

10  times. 

10  in 

100 

10  times. 

10  in  100 

10  times. 

1.  If  50  apples  buy  10  oranges,  how  many  apples  buy 
1  orange? 

2.  If  a  man  works  10  hours  a  day,  in  how  many  days 
would  he  work  60  hours? 

3.  If  40  plums  are  equally  divided  among  10  boys, 
how  many  plums  does  each  boy  receive  ? 

4.  How  many  boys'  ages,  each  10  years  old,  has  a  man 
lived  who  is  70  years  old  ? 

5.  If  a  man  spends  10  dollars  a  week,  in  how  many 
weeks  would  he  spend  thirty  dollars  ? 

6.  At  10  cents  a  quart,  how  many  quarts  of  straw- 
berries can  you  buy  for  90  cents  ? 

7.  At  10  cents  apiece,  how  many  copy-books  can  be 
bought  for  20  cents  ? 

8.  There  are  10  cents  in  a  dime;  how  many  dimes  are 
there  in  80  cents  ? 

9.  A  man  gave  away  100  cents,  a  dime  to  each  person; 
to  how  many  persons  did  he  give? 


FOR   THE    SLATE    OR   BLACKBOARD. 

10)50    10)60    10)40    10)70    10)30    10)90    10)20 


»- 


68 

DIVISION. 

LESSON    XIL 

REVIEW. 

1. 

How  many  times  3  in   12  ? 

6  in 

24? 

2. 

li 

Ln 

4? 

5  in   10? 

4  in 

8? 

3. 

10] 

n 

60? 

9  in   63? 

2  in 

18? 

4. 

4] 

n 

20? 

5  in   30? 

6  in 

42? 

6. 

8 

n 

64? 

9  in   81? 

10  in 

20? 

6. 

3 

n 

9? 

4  in    16? 

5  in 

40? 

7. 

7] 

n 

49? 

6  in  less? 

9  in 

18? 

8. 

2] 

n 

2? 

3  in     3? 

4  in 

12? 

9. 

6] 

n 

30? 

7  in   35? 

8  in 

32? 

10. 

10] 

n 

40? 

2  in    16? 

3  in 

6? 

11. 

5 

m 

50? 

6  in    54? 

7  in 

42? 

12. 

9] 

m 

54? 

10  in   50? 

2  in 

10? 

13. 

4] 

n 

24? 

5  in  less? 

6  in 

36? 

14. 

8] 

n 

16? 

9  in   36? 

10  in 

70? 

15. 

3] 

n 

30? 

4  in   40? 

5  in 

45? 

16. 

7 

m 

14? 

8  in   72? 

9  in 

72? 

17. 

2 

in 

4? 

3  in   21? 

4  in 

28? 

18. 

6 

m 

60? 

7  in   63? 

8  in 

24? 

19. 

10 

n 

80? 

2  in   20? 

3  in 

27? 

20. 

5] 

m 

25? 

6  in     6? 

7  in 

70? 

21. 

9] 

n 

90? 

10  in   90? 

2  in 

12? 

22. 

4 

n 

4? 

5  in   35? 

6  in 

12? 

23. 

7] 

n 

7? 

8  in   24? 

lin 

5? 

24. 

2 

n 

6? 

2  in     8? 

lin 

8? 

25. 

3 

n 

6? 

5  in     5? 

8  in 

8? 

26. 

9 

m 

9? 

9  in  less? 

10  in 

10? 

27. 

8 

n 

40? 

7  in   21? 

3  in 

15? 

28. 

7 

n 

56? 

2  in  less? 

6  in 

48? 

29. 

10 

n 

30? 

5  in   20? 

9  in 

27? 

30. 

4 

n 

36? 

Sin   56? 

3  in 

18? 

31. 

7 

m 

28? 

2  in   14? 

6  in 

18? 

32. 

5 

n 

15? 

9  in   45? 

10  in 

100? 

33. 

4 

m 

32? 

8  in  48? 

3  in 

24? 

34. 

8 

in 

less? 

8  in   80? 

lin 

3? 

EXERCISES.  69 


LESSON    XIIL 

PROMISCUOUS   EXERCISES. 

1.  If  you  did  not  know  the  Division  Table,  and  had 
18  cents,  how  would  you  manage  to  know  the  number 
of  oranges  that  you  could  buy  at  3  cents  apiece? 

2.  If  you  had  45  cents,  how  many  trips  could  you 
take  in  a  car  at  5  cents  a  trip  ? 

3.  With  40  cents,  how  many  pounds  of  sugar  can  I 
buy  at  8  cents  a  pound  ? 

4.  With  50  cents,  how  many  pencils  can  I  buy  at  6 
cents  apiece,  and  how  many  cents  should  I  have  left  ? 

5.  James  owes  a  man  60  cents ;  how  many  days  must 
James  work  for  the  man,  at  10  cents  a  day,  to  pay  his 
debt? 

6.  John  has  a  sled  which  he  values  at  30  cents ;  if  he 
trades  it  for  fire-crackers  at  6  cents  a  package,  how  many 
packages  should  he  receive? 

7.  A  farmer  brought  to  a  grocer  10  dozen  of  eggs  at  8 
cents  a  dozen,  and  took  his  pay  in  coffee  at  10  cents  a 
pound;  how  many  pounds  did  he  receive? 

8.  If  you  have  75  cents,  and  give  7  cents  each  to 
needy  persons,  to  how  many  persons  do  you  give,  and 
how  many  cents  have  you  left  ? 

9.  Frank,  Harry  and  Edwin  bought  a  small  wagon  for 
30  cents,  and  shared  the  cost  equally;  how  mu'^h  did 
each  pay? 

10.  They  sold  it  for  24  cents,  and  shared  the  money 
equally ;  how  much  did  each  receive  ? 

11.  A  farmer  traded  8  sheep,  at  2  dollars  a  head,  for 
4  calves ;  what  did  each  calf  cost  h'm  ? 

12.  One  man  works  for  another  6  days  at  3  dollars  a 
day,  and  is  paid  in  work  at  2  dollars  a  day;  how  many 
days'  work  should  he  receive  ? 

13.  William  gave  away  50  cents  in  five-cent  pieces,  and 
Henry  100  cents  in  dimes ;  to  how  many  persons  did 
each  give,  each  person  getting  1  piece  ? 


70  COUNTING. 


LESSON    XIV. 

f 
COUNTING. 

Make  about  a  hundred  marks  upon  the  slate,  or  black- 
board. Begin  at  one  end  of  the  row,  and  separate  it  into 
threes  by  commas ;  thus — 

I    I    I,   I    I    h   I    I    1,1    I    h&o- 

Now  count  by  threes,  saying,  three,  six,  nine,  &c. 
Count  the  same  row  downward. 

Leave  off  one  mark  at  the  end,  and  separate  the  rest 
into  threes,  and  count;  thus — 

I  ,  J    I    I  ,   I    I    I  ,    I    I    I  ,   &c.,  saying,  one,  four, 
seven,  &c. 

Count  the  same  row  downward. 

Leave  off  two  marks  at  the  end,  and  separate  the  rest 
into  threes,  and  count,  saying,  two,  five,  eight,  &c. ;  and 
count  the  row  downward. 

Make  a  row  of  a  hundred  marks,  and  separate  them 
into  fours,  and  count  by  fours  both  ways. 

Leave  off  one  mark  from  the  end,  and  count  the  rest 
hy  fours,  saying,  one,  five,  nine,  &c. 

Leave  off  two  marks  from  the  end,  and  count  the  rest 
hj  fours,  saying,  two,  six,  ten,  &c. 

Leave  off  three  marks  from  the  end,  and  count  the  rest 
hj  fours,  saying,  three,  seven,  &c. 

Make  a  row  of  a  hundred  marks,  and  separate  them 
into  fives,  and  count  hy  fives  both  ways. 

Leave  off  one  mark  from  the  end,  and  count  the  rest 
by  fives,  saying,  one,  six,  eleven,  &c. 

Leave  off  two  marks  from  the  end,  and  count  the  rest 
hy  fives,  saying,  two,  seven,  twelve,  &c. 

Leave  off  three  marks  from  the  end,  and  count  the  rest 
by  fives,  saying,  three,  eight,  &c. 

Leave  off  four  marks  from  the  end,  and  count  the  re:St 
hy  fives,  saying,  four,  nine,  &c. 

Count  these  rows  downward. 


9 i 

NOTATION   AND   NUMERATION.  71 


NOTATION  AND  NUMERATION. 


LESSON    I. 


A  UNIT  is  a  single  thing. 

A  figure  which  is  alone  expresses  units.  Thus,  if  we 
I  peak  of  6  trees,  we  mean  six  single  things  called  trees. 

There  are  only  nine  figures  that  express  number,  and 
one  figure  which  expresses  no  number y  viz. : — 

1,     2,      3,       4,     5,     6,      7,        8,       9,        0. 
One,  two,  three,  four,  five,  six,  seven,  eight,  nine,  naught. 

What  is  the  greatest  number  of  things  which  you  can 
express  with  one  figure  ?     Ans. — Nine. 

How  do  we  express  more  than  nine  ? 

Ans. — By  using  two  or  more  figures. 

How  is  ten  written  ? 

Ans. — By  the  figure  1  and  a  0  at  its  right  hand; 
thus — 10.  In  this  the  1  means  1  ten,  and  the  0  means  no 
units. 

How  much  is  1  ten,  or  once  ten?     Ans. —  Ten. 

How  much  are  ten  and  0  ?     Ans. —  Ten. 

If  1  with  0  (10)  means  1  ten  and  no  units,  what  would 
1  with  1  (11)  mean  ?     Ans. — 1  ten  and  1  unit. 

How  much  are  ten  and  one?  Ans. — Eleven;  there- 
fore 1  with  1  (11)  means  eleven.     In  like  manner, 

1  with  2  (12)  means  1  ten  and  2  units,  or  tioelve. 

1  with  3  (13)  means  1  ten  and  3  units,  or  thirteen, 

1  with  4  (14)  means  1  ten  and  4  units,  or  fourteen. 

1  with  5  (15)  means  1  ten  and  5  units,  or  fifteen. 

1  with  6  (16)  means  1  ten  and  6  units,  or  sixteen, 

1  with  7  (17)  means  1  ten  and  7  units,  or  seventeen, 

1  with  8  (18)  means  1  te^i  and  8  units,  or  eighteen. 

1  with  9  (19)  means  1  ten  and  9  units,  or  nineteen. 

How  is  twenty  written  ?     Ans. — By  the  figure  2,  with 


72  NOTATION   AND    NUMERATION. 

a  0  at  its  right  hand ;  thus — 20.     In  this  the  2  means  2 
tens,  and  the  0  means  no  units. 

How  much  are  2  tens,  or  twice  ten?     Ans. —  Twenty. 

How  much  are  twenty  and  0?     Ans. —  Twenty. 

If  2  with  0  (20)  means  2  tens  and  no  units,  what 
would  2  with  1  (21)  mean  ?     Ans. — 2  ^ens  and  1  miit. 

How  much  are  twenty  2i\i^  one?     Ans. —  Twenty-one; 
therefore  2  with  1  means  twenty-one.     Thus,  also, 
2  with  2  (22)  means  2  ^ews  and  2  wwiVs,  or  twenty-two. 
2  with  3  (23)  means  2  ^ens  and  3  wwzVs,  or  twenty-three 
2  with  4  (24)  means  2  ^e/is  and  4  w/tz^s,  or  twenty-four. 
&c.  &c.  &c. 

Note. — Let  the  pupil  be  exercised  thus  to  99. 


LESSON    II. 


How  is  one  hundred  written  ?  Ans. — By  the  figure  1 
with  two  O's  at  its  right  hand ;  thus — 100.  In  this  the 
1  means  1  hundred,  the  0  next  to  it  means  no  tens,  and 
the  last  0  means  no  units. 

How  many  tens  make  one  hundred  ?     Ans. —  Ten  tens. 

If  you  add  0  tens  and  0  units  to  a  hundred,  what  is  it 
still  ?     Ans. — One  hundred. 

If  100  means  1  hundred,  no  tens,  no  units,  what  would 

101  mean?     Ans. — 1  hundred,  0  tens,  1  unit. 

How  much  is  that  ?     Ans. — One  hundred  and  one. 
In  like  manner, 

102  means  1  hundred,  2  units,  or  one  hundred  and  two. 

103  means  1  hundred,  3  units,  or  one  hundred  and  three. 

104  means  1  hundred,  4  units,  or  one  hundred  and  fo^ir. 

105  means  1  hundred,  5  units,  or  one  hundred  and  five. 

106  means  1  hundred,  6  units,  or  one  hundred  and  si;r. 

107  means  1  hundred,  7  units,  or  <?7i6  hundred  and  seven. 

108  means  1  hundred,  8  wmVs,  or  one  hundred  and  ei^/i^ 

109  means  1  hundred,  9  units,  or  one  hundred  and  nine. 

What  does  110  mean  ?   Ans. — 1  hundred,  1  ^en,  0  units. 

How  much  are  1  hundred  and  1  ten  ?  Ans. — One  hun- 
dred and  ten;  therefore  110  means  one  hundred  and  ten. 


NOTATION   AND   NUMERATION.  73 

What  does  111  mean  ?    Ans. — 1  hundred ,  1  ten,  1  unit. 

How  much  is  that  ?  Ans. — One  hundred  and  eleven; 
therefore  111  means  one  hundred  and  eleven.  In  like 
manner,  by  adding,  we  see  that 

112  means  one  hundred  and  twelve. 

113  means  one  hundred  and  thirteen. 

114  means  one  hundred  and  fourteen. 

115  means  one  hundred  SLudJi/teen. 
&c.  &c.  &c. 

Note. — Let  the  pupil  be  exercised  thus  to  999. 


LESSON   III. 


How  is  one  thousand  written  ?  Ans. — By  the  figure 
1  with  three  O's  at  its  right  hand ;  thus — 1000.  In  this 
the  1  means  1  thousand,  and  the  rest  mean  no  hundreds^ 
no  tens,  no  units. 

How  many  hundreds  make  one  thousand  P 

Ans. — Ten  hundreds. 

If  you  add  no  hundreds,  no  tens,  no  units  to  one  thou- 
sand, what  is  the  sum  still?  Ans. — One  thousand; 
therefore  1000  means  one  thousand. 

In  like  manner,  by  adding,  we  see  that 

1100  means  1  thousand,  1  hundred,  or  11  hundred. 

1110  means  1  thousand,  1  hundred  and  ten. 

1111  means  1  thousand^  1  hundred  and  eleven. 

1112  means  1  thousand,  1  hundred  and  twelve. 
1123  means  1  thousand,  1  hundred  and  23. 
1234  means  1  thousand,  2  hundred  and  34. 
2345  means  2  thousand,  3  hundred  and  45. 
3406  means  3  thousand,  4  hundred  and  6. 
4057  means  4  thousand  and  fifty-seven. 

7009  means  7  thousand  and  nine. 

8401  means  8  thousand,  4  hundred  and  one. 

9560  means  9  thousand,  5  hundred  and  bu. 

8022  means  8  thousand  and  twenty-two. 

6000  means  6  thousand. 

9999  means  9  thousand,  9  hundred  and  99. 


ffi- 


74 


NOTATION   AND   NUMERATION. 


EXERCISES. 


Pronounce  the  following  numbers. 


7 

87 

987 

70 

870 

9870 

700 

8700 

9807 

9087 


9007 

5 

2 

4003 

807 

65 

22 

2043 

708 

465 

222 

2403 

9078 

3465 

2222 

3402 

9708 

50 

3333 

4302 

7098 

650 

4444 

3420 

7980 

560 

5555 

3024 

798 

605 

6666 

4000 

79 

506 

7777 

5400 

8907 

4056 

8888 

6540 

7654 
3821 
1283 
1823 
1382 
1832 
2562 
5622 
5226 
2652 


60  in  tlie 

600  in  the 

.  6  000  in  the 

60  000  in  the 

600  000  in  the 

6  000  000  in  the 

60  000  000  in  the 

600  000  000  in  the 

6  000  000  000  in  the 


LESSON    IV. 

6  alone  is  6  units,  or  six. 


2d  place 
3d  place 
4th  place 
5th  place 
6th  place 
7th  place 
8  th  place 
9th  place 
10th  place 


is  6  tens,  or  sixty, 
is  6  hundreds, 
is  60  hundreds, 
is  60  thousand, 
is  600  thousand. 
is  6  millions. 
is  60  millions. 
is  600  millions. 
is  6  billions. 


6  666  666  666 


Now  add  the  figures  in  each  column,  rem,embering  the 
names  of  the  figures,  and  you  see  that  the  sum  is  read  as 
follows  : — 6  billions,  666  millions,  666  thousand,  and  666. 

You  can  continue  in  this  manner,  writing  figures 
toward  the  left,  through  tens  of  billions,  hundreds  of 
billions,  trillions,  and  so  through  quadrillions,  quintil- 
lions,  sextillionSj  septillions,  octillions,  nonillions,  decil- 
lions,  &c. 

The  first  three  right-hand  figures  are  units. 

The  second  three  fif^ures  are  thousands. 


-« 


NUMERATION   AND   ADDITION. 


75 


The  third  three  figures  are  millions. 

The  fourth  three  figures  are  billions. 

The  fifth  three  figures  are  trillions. 
&c.  &c.  &c. 

Begin  at  the  right  hand  of  the  following  numhers, 
point  them  off  into  groups  of  three  figures,  and  name  the 
groups  as  you  go. 

Then  begin  at  the  left  hand,  and  pronounce  the  num- 
bers, remembering  the  names  of  the  groups. 


12506 

230034 

2660205 

10500400 

530405060 

4303202101 

9005006007 

1070080050 

2010000678 

6000302000 


7000480000 
4050600001 
1055066077 
1110220330 
2099004400 
1819202122 
2324252627 
2829303132 
3334353637 
3839404142 


1110109108 

5114113112 

2121021120 

6400003003 

8760000005 

9000008000 

605270530 

40385039 

2020303 

9876543210 


EXERCISES  m  ADDITION 


LESSON  I. 

Begin  with  the  right-hand  column,  add  each  column 
by  itself,  and  set  its  sum  below  it.  Then  pronounce  the 
whole  sum,  for  an  answer. 

(1)        (2)        (3)        (4)        (5)        (6)        (7)        (8)        (9)       aO)     (11) 

45678934573 
97849764562 


13 


»- 


76 


ADDITION. 


(12) 

as) 

%^ 

(15) 

(16) 

(17) 

(18) 

(19) 

23 

85 

8i 

47 

50 

25 

62 

45 

64 

21 

10 

20 

46 

33 

5 

68 

(20) 

631 
445 
213 

1289 

(27) 

3020 
5204 
7343 
9121 


(21) 

804 
322 
510 


(22) 

723 

104 

71 


(23) 

910 
535 
412 


(24) 

87 
601 
310 


1 

70 

600 


(26) 

567 

2 

620 


(32) 

43210 
32101 
21012 
10123 
123 


(28) 

4112 

2201 

345 

31 


(33) 

54002 
40023 
34043 
20010 
1000 


(29) 

5603 

1003 

3281 

111 


(34) 
11111 

2220 

330 
44002 
80000 


(30) 

6070 

514 

3201 

11 


(35) 

85204 
10101 
22001 
30000 
42400 


(31) 

7123 

8234 

2340 

102 


(36) 

21015 
21020 
21030 
21401 
21402 


LESSON   IL 

1.  What  is  the  sum  of  75  and  89  ?     Ans.— 164. 


First  Method. 
75 
89 

14 
15 

164 

(This  method 
is  not  used.) 


Second  Method.  Explanation. 

75  Put  the  units  of  the  num- 

gg  bers  in  the   right-hand  co- 

lumn,  and  their  tens  in  the 

.  second  column.     Then  add, 

■*-^'*  saying,  "  9  units  and  5  units 

are  14  units,  which  are  equal 

to  1  ten  and  4  units."     You 

can  write  the  4  units  under 

the  column  of  units,  and  the 

1  ten  under  the  column  of  tens,  as  in  the 

First  Method.     Then  add  the  column  of 


ADDITION. 


77 


tens,  saying,  *' 8  tens  and  7  tens  are  15  tens,"  which  are  equal  to 
one  hundred^  and  6  tens.  You  can  write  the  5  tens  under  the 
column  of  tens,  and  the  1  hundred  at  its  left.  Now  you  can  add 
these  answers,  making  164. 

But  the  method  used  by  every  one  is,  not  to  write  the  left- 
hand  figure  of  the  sum  of  a  column,  but  to  keep  it  in  mind  and 
add  it  in  with  the  next  column.  Thus,  as  in  the  Second  Method, 
9  and  5  are  14 ;  write  the  4,  and  remember  the  1  when  you  add 
the  next  column ;  1  and  8  are  9,  and  7  are  16 ;  write  the  whole, 
making  164. 

You  can  begin  at  the  top  of  each  column,  and  add  downwards^ 
if  you  prefer  to  do  so,  and  the  result  will  be  the  same. 


(2) 

(3)     (4)     (5)     (6) 

(7)     (8) 

(9) 

38 

47   64   92   55 

66   95 

73 

62 

59   37   79   88 

44   99 

37 

(10) 

ai)    (12)    (13) 

14)     (lb) 

(16) 

123 

987   306   512   706   427 

290 

456 

654    84    73 

98   357 

807 

789 

321   519    53   854   618 

342 

(17) 

as)      (19)      (20) 

(21) 

(22) 

3501 

28    135   2034 

5634 

9 

1729 

506   6247   8050 

807 

89 

5947 

3792    873   9708 

5082 

789 

7365 

400     99    201 

326 

9876 

(23) 

(24)        (25) 

(26) 

(27) 

40623 

65018    84301 

31032 

50050 

8055 

28302      9 

24051 

80004 

712 

1045    5061 

5061 

20060 

9064 

6     742 

70 

40031 

80505 

82    46307 

1040 

82 

12010 

733    2811 

41041 

60040 

3281 

46054      64 

8010 

70071 

— 

■    ■    ■  ■      » 

78                SUBTRACTION. 

(28) 

(29) 

(30) 

'(31) 

(32) 

78923 

.88 

54 

35740 

99887 

7538 

987 

196 

79300 

8998 

64216 

7878 

2983 

84000 

77665 

9988 

59585 

99847 

90000 

4433 

76543 

64463 

8866 

56000 

22110 

1988 

40530 

998 

48200 

5522 

66559 

5646 

35 

23890 

256 

EXERCISES  m  SUBTRACTION. 


LESSON  I. 


Begin  with  the  units,  take  each  figure  in  the  lower 
number  from  the  figure  above  it,  and  set  the  difference 
below;  then  pronounce  the  whole  answer. 


(1) 

79 
25 

(2)    (3)    (4) 

86   94   67 
34   61   43 

(5) 

45 
32 

(6) 

53 
21 

(7) 

68 
55 

(8)    (9) 

77   83 
45   32 

54 

ao) 

567 
234 

(11)     (12) 

695   824 
573   413 

(13) 

755 
34 

(14) 

306 
103 

as) 

840 
30 

a6) 
704 
201 

(17) 

4321 
210 

(18)       (19)       (20) 

9876   4050   8136 
5003   1030     6 

(21) 

1860 
320 

(22) 

8106 
106 

(23)        (24) 

50604    38701 
40604    11701 

(25) 

90863 
40423 

(26) 

77665 
7065 

(27) 

39408 
5206 

B 

■ "■■ 

SUBTRACTION. 

79 

(28) 

573926 
43524 

(29) 

881144 
30132 

(30) 

553377  ^ 
342356 

(31) 

2299966 
1225732 

(32) 

1223334 
211231 

(33) 

4445555 
2342345 

(34) 

6666677 
2345623 

(35) 

7777888 
4567234 

LESSON  11. 


1.  From  45  take  27. 
Written  Process. 


Explanation. 


45 

27 


We  cannot  take  7  units  from  5  units,  be- 
cause 7  is  more  than  5.     If  we  add  10  to  the 
6  units,  making  15  units,  we  can  take  7  from 
TT  15,    leaving   8.     Write   8   under   the   units. 

■*-^  Now,  because  we  add  10  to  the  upper  num- 

ber, we  can  add  1  ten  to  the  2  tens  of  the  lower  number,  to  keep 
the  difference  the  same.  Then  say,  '*1  ten  to  2  tens  is  3  tens;  3 
tens  from  4  tens  leave  1  tenJ*^  The  answer  is  1  ten  8  units^  or  18. 
Instead  of  adding  1  to  the  next  lower  figure  every  time  we 
add  10  to  an  upper  figure,  we  can  keep  the  difference  the  same 
by  taking  1  from  the  next  upper  figure.  Thus,  we  can  say,  *'  7  from 
15  leaves  8 ;  2  from  3  leaves  1." 

We  must  take  one  of  these  two  ways,  every  time  10  is  added 
to  an  upper  figure. 


(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

(8)     (9) 

(10) 

73 

96 

21 

30 

84 

70 

60   50 

40 

46 

57 

12 

17 

58 

35 

44   33 

22 

ai) 

(12) 

(13) 

(14) 

(15) 

(16) 

(17) 

280 

980 

870 

760 

650 

540 

430 

60 

81 

766 

598 

465 

359 

187 



& 

80 

SUBTRACTION. 

(18) 

(19)      (20) 

(21) 

(22)       (23) 

5906   7805   4300 

8200 

2100   1000 

1858 

998    652 

943 

888    567 

(24) 

(25) 

(26)        (27)        (28) 

10000 

10000    10000    10000    10000   1 

1234 

89 

9    7070    9999 

(29) 

(30) 

(31) 

(32) 

111111 

mill 

122222 

1333333 

77778 

55556 

44445 

333334 

(33) 

(34) 

(35) 

(36) 

102030 

405060 

708090 

9898766 

20304 

40506 

70809 

999999 

(37) 

(38) 

(39) 

(40) 

545433 

800700 

600500 

400300 

36635 

9687 

8565 

4204 

(41) 

(42) 

(43) 

(44) 

200100 

654321 

987654 

311211 

3001 

123456 

456789 

31132 

(46) 

(46) 

(47) 

(48) 

908705 

605403 

102030 

405060 

9087 

6054 

17273 

28384 

(49) 

(50) 

(51) 

(52) 

617718 

540045 

602001 

11111111100 

8929 

39008 

41000 

1234567890 

— m 

— ffi 

MULTIPLICATION.  81 


EXERCISES  IN  MULTIPLICATION. 


LESSON  I. 


By  Multiplication  we  find  the  sum  of  tlie  repetitions 
of  a  number,  without  adding  them. 

1.  What  is  the  sum  of  28  repeated  6  times  ? 

By  Addition.  By  Multiplication.  Explanation. 

28  28  Instead  of  writing  28  six 

oQ  g  times  and  adding,  we  can 

oo                    say,  "six  times  8  are  48; 

~^  o          ,  write  8  and  carry  4 ;  6  times 

28  lb8  product.  2  are  12  and  4  carried  make 

28  16;  write  alL" 
28 

168  sum. 

The  multiplicand  is  the  number  to  be  multiplied,  or 
repeated. 

The  multiplier  is  the  number  hy  which  we  multiply, 
and  shows  the  number  of  times  the  multiplicand  is  taken. 

The  product  is  the  result  of  multiplication. 

Begin  with  the  units,  and  multiply  each  figure  of  the 
multiplicand  in  order  toward  the  left,  carrying  as  in  ad- 
dition. 


(2) 

1042 

2 

(3) 

2304 
3 

(4) 

1404 
2 

(5) 

3301 
3 

(6) 

4312 
4^ 

(7) 

2443 
4 

2084 

6912 

(8) 

3545 
5 

(9) 

2656 
5 

(10) 

5747 
6 

(11) 

6878 
6 

(12) 

2389 

7 

(13) 

3476 

7 

X 

82 


MULTIPLICATION. 


a*) 

1524 

8 

as) 
3067 
8 

(16)       (17) 

9007   5600 
9     9 

(18) 

3860 
8 

(19) 

5089 
2 

(20) 

6708 
2 

(21) 

4567 
3 

(22)       (23) 

8905   5678 
3     4 

(24) 

9897 
4 

(25V 

9876 
5 

(26) 

90123 
6 

(27) 

59700 

7 

(28) 

80905 
8 

(29) 

85432 
9 

(30) 

54321 
5 

(31) 

36900 

7 

(32) 

54800 
6 

(33) 

90800 
4 

(34) 

76000 
3 

(36) 

18000 

2 

(36) 

6831 
20 

(37) 

4572 
30 

(38) 

390 
40 

(39) 

5800 
50 

(40) 

900 
700 

136620    137160    15600   290000   630000 


LESSON  II. 

If  the  multiplier  is  more  than  one  figure,  multiply  hy 
each  of  its  figures  separately,  piTt  the  first  figure  of  each 
product  under  the  figure  that  produced  it,  then  add  the 
products. 

(1)  (2)  (3) 

4602        3089        6954 
37         204  78000 


32214 
13806 

170274 


12356 
6178 

630156 


55632  * 

48678 

542412000 


I( 


r^ — ' 

MULTIPLICATION. 

83 

(4) 

1  12014 

1     '' 

(5) 

30201 
32 

(6) 

22113 
13 

(7) 

32103 
22 

(8) 

33221 
33 

1 

(9) 

_  34567 
1    '' 

ao) 

56789 
45 

(11) 
80605 
56 

a2) 

41062 
67 

(13) 

52073 

78 

"    (14) 

63084 
§    89 

(15) 

74095 
98 

(20) 

23456 
203 

(16) 

85106 
75 

(17) 

96217 
64 

(18) 

40485 
82 

P  a9) 

12345 
102 

(21) 

34567 
304 

(22) 

45678 
405 

(23) 

56789 
506 

(24) 

67809 
607 

(25) 

78901 
708 

(26) 

89012 
809 

(31) 

40506 
456 

(27) 

90123 
909 

(28) 

10203 
123 

~    (29) 

20304 
w    234 

(30) 

30405 
345 

(32) 

50607 
567 

(33) 

60708 
678 

(34) 

jL-   70809 

(35) 

11223 

881 

(36) 

34455 

772 

(37) 

66778 
653 

(38) 

89901 
542 

(39) 

65042 

1^    360 

(40) 

71390 

280 

(41) 

8290 
470 

(42) 

7500 
3900 

(43) 

64000 
2300 

K 

84 


DIVISION. 


EXERCISES  m  DIVISION. 


LESSON    I. 


By  Division  we  find  how  many  times  one  number  con- 
tains another. 

The  dividend  is  the  number  which  contains  the  other. 

The  divisor  is  the  number  contained  in  the  dividend. 

The  quotient  is  the  result  of  division,  and  shows  the 
number  of  times  the  divisor  is  contained  in  the  dividend. 

1.  Divide  62048  by  2.     Ans.— 31024. 


By  Short  Division. 
2)62048 


31024 


Explanation. 
Write  the  divisor  2  on  the  left  of  the  divi- 
dend, draw  a  line  between  them,  and  an- 
other line  under  the  dividend.  Divide  each 
figure  in  order,  beginning  at  the  left,  and 
set  each  quotient  figure  under  the  figure 
that  produced  it. 


By  Long  Division. 
2)62048(31024 
6 

2 

2 


04 
4 


8 

8 


Explanation. 
2  is  contained  in  6  three  times. 
Put  3  at  the  right  hand  of  the 
dividend.  Now  multiply  the  di- 
visor 2  by  this  quotient  figure  3, 
making  6.  Put  this  6  under  the 
6  divided,  and  subtract.  There  is 
no  remainder.  Now  bring  down 
the  next  figure  2  of  the  dividend, 
and  divide  it  as  you  did  the  6, 
and  so  on,  till  every  figure  is  di- 
vided. 


Note. — Let  the  learner  do  the  following  examples,  both  by 
Short  Division  and  Long  Division. 


DIVISION. 


85 


(2)  (3)  (4)  (5)  (6)  (7) 

2)402       2)608       3)306      3)609      4)408      4)844 


(8) 

2)2266 

(9)             ao)            (11) 
2)4468    3)3639    3)9633 

(12) 

4)4800 

(13) 

8)88888 

14) 

4)88888 

(15) 

3)99999 

ae) 
9)99999 

(17) 

3)66066 

(18) 

6)60066 

(19) 

2)60606 

(20) 

2)40404 

LESSON    II. 

1.  Divide  2358  by  2.     Ans.— 1179. 


By  Short  Division, 

2)2358 


1179 


Explanation. 
2  in  2  once ;  2  in  3  once  and  1  remains. 
Prefix  the  remainder  1  to  the  next  figure  6, 
making  15 ;  2  in  15,  7  times  and  1  remains. 
Prefix  the  remainder  1  to  8,  making  18 ;  2 
in  18,  9  times. 


By  Long  Division. 
2)2358(1179 


3 
2 

15 
14 

18 

18 


Explanation. 
When  the  remainder  1  is  shown 
by  Long  Division,  thus,  "2  from  3 
leaves  1,"  we  bring  down  the  5  to  its 
right  hand,  making  15.  This  is  the 
same  result  as  is  made  by  prefixing 
the  1  to  the  5,  in  Short  Division. 
Bringing  down  the  next  figure  to  a 
remainder,  is  used  in  Long  Division; 
prefixing  the  remainder  to  the  next 
figure,  is  used  in  Short  Division. 


86 

DIVISION. 

(2) 

3)34788 

(3) 

4)45672 

(*) 
5)64230 

(5) 

6)78936 

(6) 

7)85344 

(7) 

8)98592 

(8) 

2)357092 

(9) 

3)56940 

ao) 

4)75948 

(11) 
5)94975 

a2) 

6)95394 

as) 

7)97132 

(U) 

8)65032 
8129 

When  the  first  figure  of  an  answer  would 
be  0,  omit  it,  because  it  does  not  express 
any  value  on  the  left  hand  of  a  number. 

as) 

9)85662 

06) 

4)30356 

07) 

7)45283 

(18) 

6)23010 

,     LESSON    III. 

1.  Divide  3575  by  25.     Ans.--143. 


By  Long  Division. 


Explanation. 


107 
100 


25)3575(143  If  we  do  not  perceive  how  many 

25  times  25  is  contained  in  36,  we  can 

try  to  find  it  by  using  the  left-hand  2 
of  25,  and  the  left-hand  3  of  35  ;  thus 
— "  2  in  3  once :  once  25  is  25."  Now, 
since  the  product  25  is  less  than  35, 

and  the  remainder  10  is  less  than  the 

•^5  divisor  25,  we  know  that  1  must  be 

frc  the  true  quotient  figure.    Bring  down 

7,  making  107.     If  now  we  try  2  of 

25  in   10  of  107,  it  is  contained    6 

times .     But  if  we  multiply  25  by  5,  the  product  is  more  than 

107.     Hence  we  must  try  1  less  than  5, — viz.,  4.     The  product 

by  4  is  less  than  107,  and  the  remainder  7  is  less  than  25.   Hence 

4  is  the  true  quotient  figure. 


tt- 


-ffi 


ffi 

ffl 

DIVISION. 

87 

(2) 

24) 5376  ( 

(3)                               (4) 

32) 9984 (         43) 1806 ( 

(5) 

54) 1242 ( 

(6) 

65) 2990 ( 

(7) 

76) 5244  ( 

(8) 

87) 7656  ( 

98) 76440  ( 

(10) 

12) 19104  ( 

(11) 
13) 30485 ( 

14) 91028 ( 

15) 127545 ( 

a4) 
16) 152448  ( 

(16) 

17) 86088  ( 

(16) 

18) 55422  ( 

(17) 

19)91238( 

-./%«.  o-.?n\r  ^f>/\iHT  1  r-i  t.                When  there  is  a  /rzaZ 
102)  310845  (3047  |  51  Rem.    remainder,  it  may  beVrit- 

ten  by  itself,  as  a  remainder, 

102)  310845  (3047 AV           ^^  ^^  "^^^  ^^  P^^  ^^  ^^^  ^^S^^ 
/                         *^            hand  of  the  quotient,  with 

the  divisor  under  it. 

ao) 
123)  62313  (    , 

(20) 

234) 142100  ( 

(21) 

345) 244309 ( 

(22) 

456) 75361  ( 

(23) 

567) 84036 ( 

(24) 

678) 90062  ( 

(25) 

789) 163598  ( 

(26) 

891)402006( 

(27) 

982) 563365 ( 

<28) 

873) 701803  ( 

(29) 

705) 340062  ( 

(30) 

604) 470309 ( 

(31) 

180) 57026  ( 

(32) 

290) 129067  ( 

(33) 

370) 182089  ( 

(34) 

460) 300300  ( 
® 

(35) 

550) 400567  ( 

(36) 

640) 128871  ( 

s 

-m 


88  FRACTIONS. 


FRACTIONS. 


LESSON    I. 

1.  If  a  stick  of  candy  is  divided  into  2  equal  parts, 
wliat  is  one  part  called  ?     Ans. — One-half. 

One-half.  One-half. 

How  many  halves  has  any  thing?     Ans. — Two. 

2.  If  a  stick  is  divided  into  3  equal  parts,  what  is  one 
part  called  ?     Ans. — One-third. 

What  are  two  parts  called  ?     Ans. — Two-thirds. 

OneAhird.  OneAhird.  One-third. 

IgOgOgLlgOgOgL       '2gL-2gL'2gLlgOgOgL       IgOgOgOgOgOgL 
How  many  thirds  has  any  thing  ?     Ans. — Three. 

3.  If  a  stick  is  divided  into  4  equal  parts,  what  is  one 
part  called  ?     Ans. — One-fourth. 

What  are  three  parts  called  ?     Ans. — Three-fourths. 

One-fourth.  One-fourth.  One-fourth.  One-fourth. 

:^^^^      igag^gLigL      igogogagL      igagog^j^ 

How  many  fourths  has  any  thing  ?     Ans. — Four. 

4.  If  a  stick  is  divided  into  5  equal  parts,  what  is  one 
part  called  ?     Ans. — One-fifth. 

What  are  two  parts  called  ?     Ans. — Two-fifths. 
Three  parts  ?     Ans. — Three-fifths. 
Four  parts  ?     Ans. — Four-fifths. 

One-fifth.  One-fifth.  One-fifth,  One-fifth.  One-fifth. 

IgOgLlgL        IgOg^I^L        IgOgO^        IgOgOg^       IgOgOgL 
How  many  fifths  has  any  thing  ?     Ans. — Five. 

5.  If  a  stick  is  divided  into  6  equal  parts,  what  is  one 
part  called  ?     Ans. — One-sixth. 

Five  parts  ?     Ans. — Five-sixths. 

One-sixth.        One-sixth.        One-sixth.        One-sixth.       One-sixth.       One-sixth. 

IgOgOgL  igagL'^L  igagogL  igogagL  ig^gog?:  IgOgOgL 
How  many  sixths  has  any  thing  ?     Ans. — Six. 
How  many  sevenths  has  any  thing  ?     Ans. — Seven. 


ffi- 


FRACTIONS. 


89 


LESSON    II. 

A  FRACTION  is  a  number  expressing  one  or  more  parts 
of  a  unit. 

In  writing  a  fraction,  we  write  above  a  line  the  num- 
ber of  parts  we  mean  to  express,  and  below  the  line  the 
number  of  these  parts  in  a  unit.     Thus — 


One-half 
One-third 
One-fourth 
One-fifth 
&c. 


One-sixth  J 
One-seventh  ^ 
One-eighth  | 
One-ninth  ^ 
&c. 


4 


Three-tenths 
Four-elevenths  j-j 

Five  twenty-seconds  ^^^ 
Ten  twenty-firsts       ^^ 
&c. 


In  a  fraction  the  number  below  the  line  is  called  the 
denominator,  (that  is,  the  namer,)  because  it  names  the 
parts  into  which  the  unit  is  supposed  to  be  divided. 

In  a  fraction  the  number  above  the  line  is  called  the 
numei'ator,  (that  is,  the  number er,)  because  it  states  the 
number  of  parts  expressed  by  the  fraction. 

Pronounce  the  followinoc  fractions : — 


2  . 

3  > 
^  . 

4  f 

4  . 
^) 

5  . 
E> 

6  . 
1) 

7  . 

146  . 
3Z1> 


SI  . 

2  . 

2  . 

2  . 

2  . 

2  . 

2  . 

2  . 

-E> 

T  > 

VP 

T3> 

IZi 

7t; 

79; 

23; 

3  . 

3  . 

3  . 

3  . 

3  . 

3  . 

3  • 

Sf 

H  > 

tt; 

21; 

37; 

42; 

/?; 

4  . 

4  . 

4  . 

4  . 

4  . 

4  . 

"5  f 

TO  f 

71; 

17; 

-B^y 

03 ; 

74; 

&   . 

5  . 

5  . 

5  . 

5  . 

5  . 

^  f 

H  f 

73  ; 

Z^J 

52" ; 

7?; 

B€f; 

■gg; 

j\; 

A; 

3%} 

A; 

6%; 

6  . 

56  ; 

iS) 

B%; 

7  . 

17  . 

2^   . 

37  . 

47  . 

57  . 

67  . 

77  . 

-65) 

V^) 

"3^; 

44  ; 

Z5) 

69 ; 

5H ; 

59; 

207  . 

275  . 

42  2  . 

fif; 

7  27  . 

9  4  1 

4  0T^ 

III; 

III; 

333  ; 

14^; 

SS9; 

?47- 

Write  in  figures  the  following  fractions  : — 
Two-sevenths;  three  thirty-thirds;  six  forty-firsts; 
twenty-five  thirty-seconds ;  seventeen  nineteenths ;  eight 
forty-fifths;  ten  twentieths;  twenty  thirtieths;  thirty 
forty-sevenths;  forty  fifty-eighths;  six  sixty-seconds; 
two  twenty-ninths ;  fifty-one  seventy-fourths ;  seventy-six 
eighty-sixths. 


8* 


90  FRACTIONS. 


LESSON    III. 

A  MIXED  NUMBER  is  composed  of  one  or  more  units, 
and  a  fraction.  The  fraction  is  written  at  the  right  hand 
of  the  units ;  thus — 

Three  and  one-half  is  written  3^. 

Four  and  one-third  is  written  4|. 

Six  and  two-fifths  is  written  6|. 

Ten  and  three-eighths  is  written  10|. 

Fifteen  and  two-ninths  is  written  15|. 


Pronounce  the  followin^:  mixed  numbers  :• 


Two  and  five-sevenths.     Six  and  one-half. 
Four  and  two-thirds.     Five  and  eight-ninths. 
Three  and  one-tenth.     Seven  and  two-fifths. 
Eight  and  one-fourth.     Nine  and  five-sixths. 
Ten  and  four-elevenths.     One  and  one-twelfth. 
Thirteen  and  nineteen  twenty-fifths. 
Seventeen  and  fifteen-thirtieths. 
Nineteen  and  seven  teen-fortieths. 
Twenty-seven  and  eight  fifty-firsts. 
Thirty- two  and  nine  sixty-seconds. 
Eighty- three  and  fifty-one  fifty-thirds. 
Seventy  and  eighty  eighty-eighths. 
Sixty  and  ninety  ninety-ninths. 
Fifty  and  fifty-one  lOlsts. 
Forty  and  thirty-two  502ds. 
Fourteen  and  fourteen  803ds. 
Twenty-five  and  twenty-four  125ths. 
Eighty  and  eight  llSths. 


& 

FRACTIONS.  91 


LESSON  IV. 

1.  How  many  halves  have  3  apples?     Ans. — 6  lia,Ves. 

Two  halves.  Two  halves.  Two  halves. 

dD  3D  U 

If  1  apple  has  2  halves,  3  apples  have  3  times  2  halves, 
that  is,  6  halves. 

2.  How  do  we  find  how  many  halves  a  numher  has  ? 
Ans. — Bi/  multiphjing  the  numher  hy  2. 

3.  How  many  halves  in  4  ?  6  ?  7  ?  9  ?  10  ?  &c. 

4.  How  many  thirds  in  5  oranges  ? 
Ans. — 5  times  3  thirds,  that  is  15  thirds. 

5.  How  many  thirds    in  2  ?  3  ?  4  ?  6  ?  7  ?  &c. 

6.  How  many  fourths  in  2  ?  3  ?  4  ?  5  ?  6  ?  &c. 

7.  How  manj  fifths     in  2  ?  3  ?  4  ?  5  ?  6  ?  &c. 

8.  How  many  sixths     in  2  ?  3  ?  4  ?  5  ?  6  ?  &c. 

9.  How  many  sevenths  in  2?  3?  4?  6?  6?  &c. 

10.  How  many  eighths  in  2  ?  3  ?  4  ?  5  ?  6  ?  &c. 

11.  How  many  ninths  in  2?  3?  4?  5?  6?  &c. 

12.  How  many  to/As  in  2  ?  3?  4?  5?  6?&c. 

13.  How  many  halves  in  3  J  pears  ? 

Ans. — 3  pears  have  6  halves,  and  a  half-pear  is  1  half 
more,  that  is,  7  halves. 

14.  How  many  thirds  in  5f  pears  ? 

Ans. — 5  pears  have  15  thirds,  and  two-thirds  more  are 
17  thirds. 

15.  How  many  halves     in  41  ?  5|  ?  6 i  ?  7i  ?  &c. 

16.  How  many  thirds     in  l|  ?  2i  ?  3|  ?  4|  ?  &c. 

17.  How  many  fourths  in  1|  ?  21  ?  31  ?  4|  ?  &c. 

18.  How  many //ifAs     in  1^  ?  1§?  If?  l|?&c. 

19.  How  many  sixths     in  1^  ?  2|  ?  3|  ?  4|  ?  &c. 

20.  Ho^  many  sevenths  in  r^?  2f?  3f  ?  4f  ?  &c. 

21.  How  many  eighths  in  1|  ?  2|  ?  3|  ?  5|  ?  &c. 
Work  out  on  the  slate  or  blackboard  that 


45|  are  272 

83|  are   ^p 

142i  are   8|3 


418|  are  33^47 
562 1  are  45^01 
6215    are^V^ 


804-p3-  are  8|17 
975y%  are  ^\\^^ 
423/^  are   ^771 


92 


FRACTIONS. 


LESSON    V. 


1.  How  many  whole  apples  in  6  half-apples  ? 

Ans. — Since  2  halves  are  1  whole  apple,  6  halves  are  as  many 
apples  as  2  halves  are  contained  times  in  6  halves ;  that  is,  3 
whole  apples. 

I?    \^?    ^/?  ^^'^?  &C, 

I  ?     L^  ?     L6  ?    2_0  ?    2^4  ?  &c. 

5.  How  many  units  in  K^  ?   U  ?  %o  ?  25  ?   so  ?  &c. 

6.  How  many  units  in  ^^^  ?   \^  ?  ^  ?  3^0  ?   3^6  ?  &c. 


2.  How  many  units  in 

3.  How  many  units  in 

4.  How  many  units  in 


; 
I? 

6? 


7.  How  many  units  in  ^^^  ? 


28? 


V? 


8.  How  many  units  in  3^2  ?  4^8  ?  6^4  ?  8^0  ?  7^2  ? 

9.  How  many  units  in  \'7?  4^5?  6^3?  5^4?  8^1  ?  &c. 

10.  Howmanyunitsin  |g?  fg?  fg?  |o?  |o?  &c. 

11.  What  is  one-half  of  10? 

Ans. — 5.   We  find  one-half  of  a  number  hy  dividing  it  by  2. 


V?  'V?&c. 


12.  What  is 

13.  What  is 

14.  What  is 

15.  What  is 

16.  What  is 

17.  What  is 

18.  What  is 

19.  What  is 

20.  What  is  ^ 

21.  What  is 


1 

I  of 


iof 
^of 

4  of 

I  of 
iof 
Vof 
I  of 


?  12? 
15?  24? 

8?  24? 
20?  35? 
30?  24? 
21?  28? 
32?  72? 


of  6?  8 
9? 
16? 
10? 
18? 
42? 
64? 

81?  72?  45? 
20?  30?  40? 
12? 


18?  &c. 
27?&c. 
36?  &c. 
40?  &c. 
12?  &c. 
14?  &c. 
40?  &c. 
63?&c. 
50?  &c. 


Ans.— 8. 


Analysis. — One-third  of  12  is  4,  and  two-thirds  of  12  must 
be  2  times  4,  that  is,  8. 


22.  What 

23.  What 

24.  What 

25.  What 

26.  What 

27.  What 

28.  What 

29.  What 


s  I  of 


8?  12? 
s|of  10?  15? 
'  of  10?  15? 
of  6?  12? 
of  7?  14? 
of  35?  42? 
of  8?  16? 
of    9?  18? 


16?  20?  &c. 
20?  25?  &c. 
20?  25?  &c. 
24?&c. 

28?  &c. 
56?  &c. 
32?  &c. 


18? 
21? 
49? 
24? 


27?  36?  &c. 


FRACTIONS.  93 


LESSON  VL 

I.  What  is  iof  7? 

Ans. — 3J.  Since  J  of  6  is  3,  and  J  of  the  remaining  1  is  J, 
J  of  7  must  be  3  J.  This  explains  why  we  put  the  divisor  under 
the  last  remainder  in  division. 

2.  What  is  i  of  8?  10?  11?  14?  16?  &c. 

3.  What  is  i  of  5?     7?  13?  15?  18?  &c. 

4.  What  is  I  of  6?     7?     8?     9?  12?  &c. 
6.  What  is  i  of  7?  11?  17?  19?  22?  &c. 

6.  What  is  4  of    8?     9?  10?  11?  12?  &c. 

7.  What  is  ^  of   9?  11?  13?  15?  19?  &c. 

8.  What  is  ^  of  10?  11?  13?  14?  23?  &c. 

9.  How  many  units  in  |  ?     Ans. — 3  J. 

Analysis. — Since  2  halves  equal  1  unit,  7  halves  equal  as 
many  units  as  2  is  contained  times  in  7. 

10.  How  many  units  in    ^  ?   y  ?   ^  ?  1^5  ?   rr  ?  &c. 

II.  How  many  units  in    I  ?     |?     -J?  |?     |?&c. 

12.  How  many  units  in    f  ?     |  ?   '/  ?  V  ?  ^8  ?  &c. 

13.  How  many  units  in    i?   V^     f?  V?  V  ?  &«. 

14.  How  many  units  in    |  ?   \9?  %^  ?  3_9  ?  4^3  ?  &c. 
1.  >.  How  many  units  in  ^^  ?  ^  ?   s^i  ?  ^^^  ?  ^  ?  &c. 

16.  How  much  is  3  times  |?     Ans. — ^3^,  or  2|. 

17.  How  much  is  4  times  f  ?  |  ?    f  ?  /j  ?  &c. 

18.  How  much  is  5  times  4?  |?  /j?  /^?  &c. 

19.  How  much  is  6  times  J?  4?  fj?  -f^'i  &c. 

20.  How  much  is  7  times  I  ?  |  ?    |  ?    |  ?  &c. 

21.  How  much  is  8  times  I?  I?    4?    5?&c. 

22.  What  is  I  of  7? 

Ans.— 4§.  Since  J  of  7  is  2J,  2  thirds  of  7  must  be  2  times 
2J.    Now,  2  times  2  are  4,  and  2  times  J  are  f :  4  and  f  are  4f . 

23.  What  is  I  of  4?  10?  13?  16?  19?  &c. 

24.  What  is  I  of  5?     6?     7?     9?10?ll?&c. 

25.  What  is  I  of  6?     7?     8?     9?ll?12?&c. 

26.  What  is  |  of  6?     7?     8?     9?  11?  12?  &c. 

27.  What  is  I  of  7?     8?     9?  10?  11?  13?  &c. 

28.  What  is  f  of  8?     9?  10?  11?  12?  13?  &c. 

29.  What  is  I  of  9?  10?  11?  12?  13?  14?  &c. 


© 

I  94  FRACTIONS. 


LESSON    VII. 

1.  How  many  are  ^  and  ^?     Ans. — |,  or  1. 

2.  How  many  are  |  and  J  ?  i  and  f  ?  |  and  f  ? 

3.  How  many  are  |  and  |  ?  |  and  |  ?  |  and  |  ? 

4.  f  and    |?/oand/^?     I  and    |?     |  and    |? 

5.  j\  and  If?     I  and    |?  /^  and  1^  ?  f4  and  f|? 

6.  V  and  V?    S'  and  y  ?  jf  and  1|?  |o  and  fg? 

7.  land    I  and    f?     |  and     |  and     |? 

8.  Yj  and  ii  and  f«?  j|  and  jf  and  ji  ? 

9.  jl  and  jf  and  j§  and  |^  and  jf  and  /^? 

10.  II  and  II  and  ||  and  ||  and  i|  and  |g? 

11.  From    I  take    f .     Ans.— |. 

12.  From   -|  take   |.  From  |  take   |.  From  |  take  J. 

13.  From   |  take   |.  From   f  take   |.  From  |  take  I. 

14.  From  |  take   f .  From   |  take  |.  From  |  take  |. 

15.  From  |  take  |.  From  ^  take   |.  From  |  take   |. 

16.  From /_  take  y%.  From /^j  take yS^.  From /^  take  y^. 

17.  From  y\  take  y\.  From  j\  take /_.  From  |^  take -jfij-. 

18.  From  -^^  and  ^^^  take  j%  and  -j^^. 

19.  From  ||  and  ||  take  ||  and  j%. 

20.  From  ||  and  |f  and  ||  take  ff  and  y^^  and  /_. 

21.  What  part  of  3  is  2  ?     Ans.— f . 

Analysis. — Since  1  unit  is  J  of  3  units,  2  units  must  be  2 
times  J  of  8  units ;  that  is,  f  of  3. 

22.  What  part  of  4  is  3  ?  What  part  of  5  is  4? 

23.  What  part  of  5  is  3  ?  What  part  of  5  is  2? 

24.  What  part  of  6  is  5?  What  part  of  7  is  5? 

25.  What  part  of  7  is  6?  What  part  of  7  is  4? 

26.  What  part  of  10  is  5?  Ans.— y^^,  or  A. 

Why  is  5  one-half  of  10  ?     Ans. — Because  ^  is  con- 
tained in  1  two  times,  and  5  is  contained  in  10  two  times. 

27.  What  part  of    6  is  2?     What  part  of   6  is  3? 

28.  What  part  of    6  is  4  ?     What  part  of  15  is  3  ? 

29.  What  part  of  12  is  3  ?     What  part  of  18  is  3  ? 


&c.  &c. 


FRACTIONS.  95 


LESSON  VIII. 

1.  If  4  melons,  of  equal  price,  cost  12  cents,  how  many 
cents  do  3  of  them  cost?     Ans.  9  cents. 

Analysis. — If  4  melons,  of  equal  price,  cost  12  cents,  1  melon 
costs  J  of  12  cents;  that  is,  3  cents.  If  1  melon  costs  3  cents, 
3  melons  of  the  same  price  cost  3  times  3  cents ;  that  is,  9  cents. 

2.  If  3  pounds  of  sugar  cost  27  cents,  how  much  will 

5  pounds  of  the  same  cost  ? 

3.  If  2  pounds  of  coffee  cost  24  cents,  how  much  will 

6  pounds  of  the  same  cost  ? 

4.  If  3  pounds  of  beef  cost  30  cents,  how  much  will 

2  pounds  of  the  same  cost  ? 

/  b.  If  4  yards  of  muslin  cost  32  cents,  how  much  will 
9  yards  of  the  same  cost  ? 

6.  If  a  man,  walking  regularly,  walks  24  miles  in  8 
hours,  how  far  does  he  walk  in  5  hours  ? 

7.  If  a  boat,  sailing  regularly,  goes  44  miles  in  4 
hours,  how  far  does  it  sail  in  3  hours  ? 

8.  If  10  boxes  of  raisins  cost  20  dollars,  what  cost  7 
boxes  of  the  same  ? 

9.  If  4  oranges  cost  10  cents,  what  do  3  of  them  cost? 
What  would  6  of  the  same  kind  cost  ? 

10.  If  4  pencils  cost  25  cents,  what  would  12  of  the 
same  cost  ?    What  would  3  of  them  cost  ? 

11.  If  3  yards  of  cloth  cost  9  dollars,  how  much  of  the 
same  can  you  buy  for  10  dollars  ? 

12.  If  4  barrels  of  cider  cost  8  dollars,  how  many 
barrels  of  it  can  you  buy  for  11  dollars  ? 

13.  If  2  barrels  of  apples  cost  5  dollars,  how  much  will 

3  barrels  cost  ?  4  barrels  ?   5  barrels  ? 

14.  If  5  pounds  of  coffee  cost  75  cents,  how  much  of 
the  same  can  be  bought  for  65  cents  ? 

15.  At  the  rate  of  80  cents  for  8  pounds  of  starch, 
how  much  can  be  bought  for  25  cents  ? 

16.  A  merchant  bought  40  barrels  of  potatoes,  and 
sold  at  one  time  \  of  them,  and  at  another  time  |  of  the 
remainder;  how  many  had  he  left? 


96  FRACTIONS. 


LESSON   IX. 

1.  If  i  of  a  pound  of  tea  is  worth  10  cents^  liow  much 
is  a  whole  pound  of  the  same  worth  ? 

Analysis. — If  ^  of  a  pound  of  tea  is  worth  10  cents,  |  of  a 
pound,  that  is,  a  whole  pound,  will  be  worth  5  times  10  cents, 
that  is,  50  cents. 

2.  If  I  of  a  yard  of  muslin  costs  2  cents,  how  much 
does  a  whole  yard  cost  ?     2  yards  ?     3|  yards  ? 

3.  If  -1  of  a  yard  of  silk  costs  40  cents,  how  much 
does  a  whole  yard  cost  ? 

4.  If  ^  of  a  pound  of  honey  costs  10  cents,  how  much 
does  a  whole  pound  cost?     2  pounds?     4^  pounds? 

5.  At  the  rate  of  2  miles  in  half  an  hour,  how  fa'* 
would  a  man  walk  in  4  hours  ? 

6.  At  the  rate  of  3  dollars  for  |  of  a  yard  of  cloth, 
how  much  will  5  yards  cost  ? 

7.  At  the  rate  of  8  cents  for  |  of  a  dozen,  how  much 
will  9  dozen  of  eggs  cost  ? 

Analysis. — If  J  of  a  dozen  of  eggs  cost  8  cents,  |  will  cost  J 
of  8  cents,  that  is,  2  cents.  If  ^  of  a  dozen  costs  2  cents,  a 
whole  dozen  will  cost  5  times  2  cents,  that  is,  10  cents,  and  9 
dozen  will  cost  9  times  10  cents,  that  is,  90  cents. 

8.  At  the  rate  of  9  cents  for  |  of  a  pound  of  coffee, 
how  much  will  9  pounds  cost  ? 

9.  At  the  rate  of  6  dollars  for  |  of  a  barrel  of  flour, 
how  much  will  5  barrels  cost  ? 

10.  When  |  of  a  certain  school  were  present,  there 
were  30  pupils ;  what  was  the  whole  number  at  school  ? 

11.  If  f  of  the  cost  of  a  watch  is  60  dollars,  how 
much  would  5  such  watches  cost  ? 

12.  If  I  of  a  quire  of  paper  cost  14  cents,  how  much 
would  10  quires  of  the  same  cost? 

13.  At  the  rate  of  28  dollars  for  ^  of  a  month,  how 
much  would  a  person  spend  in  6  months  ? 

14.  If  I  of  a  bushel  of  clover-seed  cost  3  dollars,  how 
much  does  ^  of  a  bushel  cost  ? 

15.  If  6liimes  a  number  is  72,  what  is  |  of  it? 


TABLES.  97 


TABLES 

OF  MONET,  WEIGHTS,  AND  MEASURES. 


LESSON    I. 

UNITED    STATES    MONEY. 

10  mills  (marked  m.)  make  1  cent  marked  ct. 

10  cents                           "      1  dime  "        d. 

10  dimes                          "      1  dollar  "        $ 

10  dollars                        "      1  eagle  "        E. 

1.  How  many  mills  are  there  in  2  cents?  3  cents?  &c. 

2.  How  many  dimes  are  there  in  2  dollars  ?  3  dollars  ?  &c. 

3.  How  many  dollars  are  there  in  2  eagles  ?  3  eagles  ?  &c. 

4.  How  many  cents  are  there  in  20  mills  ?  30  mills  ?  &c. 

5.  How  many  dimes  are  there  in  20  cents  ?  30  cents  ?  &c. 

6.  How  many  eagles  are  there  in  20  dollars  ?  30  dollars?  &c. 

7.  How  many  mills  are  there  in  ^  of  a  cent  ? 

8.  How  many  mills  are  there  in  |  of  a  cent  ?  |  ?  <&c. 

9.  How  many  mills  are  there  in  ^  of  a  cent  ?  |  ?  |  ?  &c. 

10.  How  many  mills  are  there  in  1|  cents  ?  21  ?  &c. 

11.  How  many  mills  are  there  in  2i  cents  ?  3|  ?  &c. 

12.  How  many  cents  are  there  in  |  of  a  dime  ?  4  ?  &c. 

13.  How  many  cents  are  there  in  2i  dimes?  3|r  &c. 

14.  How  many  cents  are  there  in  10  dimes?  5  dimes  ?  &c. 

15.  How  many  cents  are  there  in  7^  dimes?  8|  ?  &c. 

16.  How  many  cents  are  there  in  1  dollar  ? 

17.  How  many  cents  are  there  in  2  dollars  ?  &c. . 

18.  How  many  cents  arc  there  in  i  of  a  dollar  ?  |  ?  &c. 

19.  How  many  cents  are  there  in  i  of  a  dollar  ?  |  ?  &c. 

20.  How  many  dollars  in  |  of  an  eagle  ?  |  ?  &c. 

21.  How  many  dollars  in  2  eagles?  2i  eagles?  &c. 

22.  How  many  dollars  in  1000  mills  ?  100  cents  ?  &c. 


-e 


H— ^ Q 

98  TABLES. 


LESSON  II. 

ENGLISH   MONEY. 

4  farthings  (qr.  or  f.)  raake  1  penny  (d.) 
12  pence                              "      1  shilling  (s.) 

20  shillings  "     1  pound  or  sovereign  (X) 

21  shillings  "     1  guinea  (g^in.) 

5  shillings  "      1  crown. 

1.  How  many  qr.  in  2  d.  ?  3d.?  4  d.  ?  5  d.  ?  6  d.  ?  &c. 

2.  How  many  d.  in  2  s.  ?  3  s.?  4  s.?  5  s.?  6  s.?  &c. 

3.  How  many  s.  in  2  X?  3  £?  4  X?  5  X?  6  X?  &c. 

4.  Howmany  d.inl2f.?  20  f.?  28  f.  ?  32f.?  36f.?&c. 

5.  How  many  s.  in  36  d.  ?  60  d.  ?  72  d.  ?  84  d.  ?  96  d.  ?  &c. 

6.  Howmany  X  in  30  s.?  45  s.?  55s.?  70s.?  95s.?&c. 

7.  Howmany  f.  in  }^d.?  |d.?  |d.?  1-Jd.?  f"  '  "  " 

8.  How  many  d.  in  ^  s.  ?  |  s.  ?  |  s.  ?  1 J  s.  ?  2\ 

9.  How  many  s.  in  I  X?  §X?  |X?  llX?  2| 
10.  How  many  shillings  in  half  a  crown  ? 


?&c. 


LONG    OR    LINEAR    MEASURE. 

12  inches  (in.)  make  1  foot  (ft.) 

3  feet  "      1  yard  (yd.) 

5i  yards,  or  16^  feet,  "      1  rod,  pole,  or  perch  (rd.) 

40  rods  "      1  furlong  (fur.) 

8  fur.,  or  320  rods,      "      1  mile  (m.) 

3  miles  "      1  league  (lea.) 

1.  How  many  inches  in  2^  ft.  ?  3|  ft.  ?  4|  ft.  ?  5|  ft.  ?  &c. 

2.  How  many  feet  in  2  yd.?  31  yd.?  4f  yd.?  5lyd.?&c. 

3.  How  many  yards  in  36  ft.  ?  48  ft.?  21ft.?  24  ft.  ?  &c. 

4.  How  many  yards  in  2  rd.  ?  4  rd.  ?  6  rd.  ?  8  rd.  ?  &c. 

5.  How  many  rods  in  2  m.  ?  1^  m.  ?  3|  m.  ?  41  m.  ?  &o. 

6.  How  many  miles  in  6  lea.  ?  12  lea.  ?  30  lea.  ?  &c. 

7.  How  many  leagues  in  5  m.  ?  7  m.?  8  m.?  &c. 

8.  How  many  feet  in  10  rd.  ?  20  rd.?  30  rd.  ?  40  rd.? 


m J 

TABLES.  99 


LESSON  III. 

ENGr)fEERS'    AND   SURVEYORS^    MEASURE. 

7j%\  inches  (in.)  make  1  link  (1.) 

25  links  ^^      1  pole,  or  rod  (p.) 

4  poles,  or  66  feet,  "      1  chain  (ch.) 

10  chains  "      1  furlong         (fur.) 

8  furlongs,  or  80  chains,     "      1  mile  (m.) 

1.  How  many  links  in  2  p.  ?  3  p.  ?  4  p.  ?  5  p.  ?  &c. 

2.  How  many  links  in  ^  p.  ?  2^  p.  ?  3|  p.  ?  4|  p.  ?  &c. 

3.  How  many  poles  in  2  ch.*?  2^  ch.  ?  3|  ch.  ?  4|  ch.  ?  &c. 

4.  How  many  feet  in  1|  ch.  ?  2  ch.  ?  4  ch.  ?  5  ch.  ?  &c. 

5.  How  many  chains  in  2  fur.  ?  3|  fur.  ?  4|  fur.  ?  &c. 

6.  How  many  furlongs  in  2^  m.  ?  3|  m.  ?  5|  m.  ?  &c. 

7.  How  many  chains  in  3  J^  m.  ?  4^  m.  ?  6|  m.  ?  &c. 

8.  How  many  miles  in  720  ch.?  800  ch.?  320ch.?&c. 

9.  How  many  miles  in  32  fur.  ?  64  fur.  ?  80  fur.  ?  &c. 
10.  How  many  chains  in  12  p.  ?  20  p.  ?  36  p.  ?  &c. 

CLOTH   MEASURE. 

2i  inches  (in.)  make  1  nail  (na.) 

4  nails,  or  9  inches,     "  1  quarter  of  a  yard   (qr.) 

4  quarters  "  1  yard  (j^O 

3  quarters  "  1  Flemish  ell. 

4  qr.  11  in.  "  1  Scotch  ell. 

5  qr.  "  1  English  ell. 

6  qr.  "  1  French  ell. 

.  ?  3  qr.  ?  5  qr.  ?  6  qr.  ?  &c. 
|yd.?l^yd.?l|yd.?&c. 
yd.?iyd.?|yd.?&c. 
, ^  _. .  _  ^  i.?  3  yd.?  4yd.?  &c. 

5.  How  many  feet  in  li  yd.  ?  2|  yd.  ?  3|  yd.  ?  4|  yd.  ?  &c. 

6.  How  many  yards  in  36  in.  ?  54  in.  ?  72  in.  ?  &c. 

7.  How  many  yards  in  3  ft.  ?  4  ft.  ?  5  ft.  ?  6  ft.  ?  &c. 


100  TABLES. 


LESSON  IV. 

SURFACE   OR   SQUARE   MEASURE. 

A  square  inch  is  a  square  surface  1  inch  long  and  1 
inch  broad.  A  square  foot  is  a  square  surface  1  foot 
long  and  1  foot  broad.  A  square  yard  is  a  square  sur- 
face 1  yard  long  and  1  yard  broad.  A  square  rod-is  a 
square  surface  1  rod  long  and  1  rod  broad.  A  square 
mile  is  a  square  surface  1  mile  long  and  1  mile  broad. 

144  square  inches  (sq.  in.)  make  1  square  foot      (sq.  ft.) 

9  square  feet  "  1  square  yard     (sq.  yd.) 

30 i  square  yards,  or  ")  a  ^  square  rod,  or  ^p  . 

272 i  square  feet           j  pole,  or  perch  ^    '^ 

40  square  rods  ^^  1  rood                 (R.) 

4  roods,  or  10  sq.  ch.  "  1  acre                  (A.) 

640  acres  "  1  square  mile.    (sq.  m.) 

1.  How  many  square  inches  in  a  page  6  inches  long 
and  4  inches  broad  ?  Ans.  24.  To  find  the  quantity  of 
any  square  surface^  we  multiply  its  length  by  its  breadth^ 
using  the  same  liriear  units  for  both. 

2.  How  many  square  inches  in  2  square  feet  ?  In  a 
surface  2  feet  square  ? 

3.  How  many  square  feet  in  2  square  yards?  In  a 
surface  2  yards  square  ? 

4.  How  many  square  rods  in  3  roods  ? 

5.  How  many  square  rods  in  1  acre  ?     2  acres  ? 

6.  How  many  square  miles  in  1280  acres  ? 

7.  How  many  acres  in  2  square  miles  ?  3  square  miles  ? 

8.  How  many  acres  in  320  square  rods  ? 

9.  How  many  acres  in  a  farm  800  rods  long  and  80 
rods  broad  ? 

10.  How  many  square  feet  in  a  floor  16^  feet  long  and 
12  feet  broad  ?     How  many  square  yards  ? 

11.  How  many  square  inches  in  ^  of  a  square  foot  ? 


9 

TABLES.  101 


LESSON  V. 

SOLID   OR   CUBIC    MEASURE. 

A  cube  is  a  body  having  six  square  surfaces. 

A  cubic  inch  is  a  cube,  each  of  whose  edges  is  an  inch 
long. 

A  cubic  foot  is  a  cube,  each  of  whose  edges  is  a  foot 
long. 

A  cubic  yard  is  a  cube,  each  of  whose  edges  is  a  yard 
long. 

1728  cubic  inches  (cu.  in.)  make  1  cubic  foot  (cu.  ft.) 
27  cubic  feet  "      1  cubic  yard  (cu.  yd.) 

'  128  cubic  feet  "      1  cord  of  wood      (C.) 

42  cubic  feet  "      1  ion  of  shipping. 

1.  How  many  cubic  inches  in  a  stick  10  inches  long, 

3  inches  broad,  and  2  inches  thick  ? 

Ans.  60.  To  find  ike  cubical  quantity  of  any  square 
thing,  we  multiply  its  length  by  its  breadth ,  and  that 
product  by  its  thickness, 

2.  How  many  cubic  inches  in  2  cu.  ft.  ?  3  cu.  ft.  ?  &c. 

3.  How  many  cubic  feet  in  2  cu.  yd.  ?  3  cu.  yd.  ?  &c. 

4.  If  a  load  of  wood  is  8  feet  long,  4  feet  broad,  and 

4  feet  high,  how  much  wood  is  it  ? 

5.  If  a  ship  can  carry  1000  tons,  how  many  cubic  feet 
are  allowed  for  her  load  ? 

6.  If  a  cellar  is  80  feet  long,  30  feet  broad,  and  5  feet 
deep,  how  many  cubit  feet  of  earth  were  dug  oiit  ? 

7.  How  many  cubic  feet  in  a  room  18  feet  long,  15  feet 
broad,  and  12  feet  high  ?     How  many  cubic  yards  ? 

8.  How  many  cubic  inches  in  a  box  3  feet  long,  2  feet 
wide,  and  2  feet  high  ? 

9.  How  many  cords  of  wood  can  be  packed  in  a  shed 
24  feet  long,  8  feet  wide,  and  8  feet  high  ? 

10.  How  many  cubic  feet  of  water  in  a  full  cistern  10 
feet  long,  7  feet  wide,  and  6  feet  deep  ? 


1^ ^ 

102  TABLES. 


LESSON    VL 

AVOIRDUPOIS  WEIGHT. 

Avoirdupois  Weight  is  used  in  weighing  almost  all 
articles  taken  in  large  quantity,  such  as  groceries,  &c. 

16  drams  (dr.)  make  1  ounce                  (oz.) 

16  ounces  "      1  pound                 (lb.) 

25  pounds  '^      1  quarter                (qr.) 

4  quarters,  or  100  lbs.  "      1  hundredweight(cwt.) 

20  cwt.  or  2000  lbs.  "     1  ton                      (T.) 

1.  How  many  drams  in  2  oz. ?  4  oz.?  5  oz.?  6  oz. ?  &c. 

2.  How  many  ounces  in  2  lb.?  3  lb.?  4  lb.?  5  lb.?  &c. 

3.  How  many  pounds  in  2  qr.  ?  3  qr.  ?  5  qr.  ?  6  qr.  ?  &c. 

4.  How  many  quarters  in  2  cwt.  ?  3  cwt.  ?  4  cwt.  ?  &c. 
6.  How  many  hundredweight  in  2  T.?   3  T.?   4  T.?  &c. 

6.  How  many  cwt.  in  8  qr.  ?  24  qr.  ?  32  qr.  ?  &c. 

7.  How  many  lb.  in  2  tons?  3  tons?  7  tons?  &c. 

8.  How  many  cwt.  in  300  lb.?   1000  lb.?    1500  lb.?  &c. 

9.  How  many  oz.  in  32  dr.?  48  dr.?  64  dr.?  &c. 


TROY  WEIGHT. 

Troy  Weight  is  used  in  weighing  coins,  precious  metals, 
jewels,  and  liquors. 

24  grains  (gr.)        make  1  pennyweight  (pwt.) 
20  pennyweights         "      1  ounce  (oz.) 

12  ounces  "      1  pound  (lb.) 

The  ounce  and  pound  of  Troy  Weight  are  not  the  same 
weights  as  the  ounce  and  pound  Avoirdupois. 

1.  How  many  gr.  in  2  pwt.?  3  pwt.  ?  4  pwt.?  &c. 

2.  How  many  pwt.  in  2  oz.  ?  3  oz.  ?  4  oz.  ?  &c. 

3.  How  many  oz.  in  2  lb.?  3  lb.?  4  lb.?  &c. 

4.  How  many  oz.  in  Hb.?  i  lb.?  IJ  lb.?  &c. 


9 — ■ 9 

TABLES.  103 


LESSON  VIL 

apothecaries'  weight. 
Apotliecaries'  Weight  is  used  in  medical  prescriptions. 
20  grains  (gr.)  make  1  scruple  (9) 


3  scruples  "      1  dram      (3 

8  drams  "      1  ounce     (J) 

12  ounces  "      1  pound    (ib) 

In  this  weight  the  grain,  ounce,  and  pound  are  the 
same  as  in  Troy  Weight. 

1.  How  many  gr.  in  2  3  ?    3  9?  49?  5  9  ?  &c. 

2.  How  many  9   in  2  5?    3  s^?   4  3?   5  5?  &c. 

3.  How  many  3    in  2  g  ?    3  §  ?   4  g  ?  5  §  ?  &c. 

4.  How  many  ^    in  2  ib  ?  3  ib  ?  4  tb?  5  ib  ?  &c. 
6.  How  many  ib  in  60  g  ?  72  g  ?  84  g  ?  &c. 

6.  How  many  g    in  48  5?  56  5?  64  3?  &c. 

7.  How  many  5   in  18  9  ?  21  9  ?  24  9  ?  &c. 

8.  How  many  9  in  100  gr.?  140  gr.?  180  gr.?  &c. 


apothecaries  fluid  measure. 

Apothecaries'  Fluid  Measure  is  used  in  measuring  the 
fluid  portions  of  medical  prescriptions. 

60  minims  (TTL)  make  1  fluidrachm  (f^;) 
8  fluidrachms       "      1  fluidounce  (fg; 

16  fluidounces        "      1  pint  (0.) 

8  pints  "      1  gallon  (Cong.) 

1.  How  many  minims  in  2  f^?    3  %?   4  %?  &c. 

2.  How  many  f^  in  2  fg  ?    3  f g  ?    4  f g  ?  &c. 

3.  How  many  fg  in  2  pints?    3  pints?    4  pints?  &c. 

4.  How  many  pints  in  2  gallons?    3  gallons?  &c. 

5.  How  many  f^  in  240  fit?    300  IT^?  &c. 

6.  How  many  f  J  in  64  £5  ?    72  f^  ?  &c. 


104  TABLES. 


LESSON   VIII. 

LIQUID   OR  WINE    MEASURE. 

Wine  Measure  is  used  in  measuring  the  bulk  of  all 
kinds  of  liquids. 

4  gills  (gi.)  make  1  pint      (pt.) 
2  pints  "       1  quart    (qt.) 

4  quarts  "      1  gallon  (gal.) 

1.  How  many  gills  in  2  pints?    3  pints?  &c. 

2.  How  many  gills  in  1^  pints?    4i  pints?  &c. 

3.  How  many  pints  in  2  quarts?    3  quarts?  &c. 

4.  How  many  pints  in  5^  quarts?    10 i  quarts?  &c. 

5.  How  many  quarts  in  2  gallons  ?    3  gallons  ?  &c. 

6.  How  many  gallons  of  wine  would  10  barrels  hold, 
each  barrel  holding  31^  gallons? 

7.  How  many  gallons  of  oil  would  20  barrels  hold, 
each  barrel  holding  40  gallons  ? 

8.  How  many  gallons  of   syrup  would   8  hogsheads 
hold,  each  hogshead  holding  63  gallons? 

9.  How  many  gallons  of  wine  would  5  pipes  hold, 
each  pipe  holding  126  gallons  ? 

10.  How  many  gallons  of  molasses  in  12  casks,  each 
cask  holding  84  gallons? 


BEER    MEASURE. 

Beer,  ale,  and  milk  are  sometimes  measured  with  ves- 
sels larger  than  those  used  for  other  liquids. 

2  pints    make  1  quart. 
4  quarts     "     1  gallon. 

This  gallon  is  282  cubic  inches  in  capacity,  but  the 
wine  gallon  is  only  231  cubic  inches. 

In  England  the  gallon  for  all  liquids  is  277j%'^|j%  cu.  in. 


a 


TABIiES.  105 


LESSON    IX. 

DRY    MEASURE. 

Dry  Measure  is  used  in  measuring  such  things  as  grain, 
truits,  salt,  &c. 

2  pints  (pt.)  make  1  quart    (qt.) 
8  quarts  '^      1  peck     (pk.) 

4  pecks  "      1  bushel  (bu.) 

The  pint  and  quart  of  dry  measure  are  not  the  same  as 
those  of  Liquid  Measure. 

1.  How  many  pints  in  2  qt.  ?  3  qt.  ?  4  qt.  ?  &c. 

2.  How  many  quarts  in  2  pk.  ?  3  pk.  ?  4  pk.  ?  &c. 

3.  How  many  pecks  in  2  bu.  ?  3  bu.  ?  4  bu.  ?  &c. 

4.  How  many  bushels  in  24  pk.  ?  36  pk.  ?  40  pk.  ?  &c. 

5.  How  many  pecks  in  32  qt.  ?  48  qt.  ?  64  qt.  ?  &c. 

6.  How  many  quarts  in  12  pt.  ?  24  pt.  ?  30  pt.  ?  &c. 

7.  How  many  quarts  in  3  J  pk.  ?  4i  pk.  ?  5|  pk.  ?  &c. 


ANGULAR   OR   CIRCULAR    MEASURE. 

Portions  of  the  circumference  of  a  circle  are  expressed 
as  parts  of  the  whole  circumference,  and  not  with  refer- 
ence to  any  absolute  length. 

60  seconds  (")  make  1  minute  (') 

60  minutes  "      1  degree  (°) 

360  degrees  "      1  circumference  (C) 

Hence,  the  size  of  a  degree  depends  upon  the  size  of 
the  circle. 

1.  How  many"  in  2'?    3'?    47    57    &c. 

2.  How  many'  in2°?   3°?   4°?   5°?  &c. 

3.  How  many  °  in  2C?  3C?  40?  50?  &c. 

4.  Howi  any°in-^0?  iO?  iO?  |0?  &c. 

5.  How  many  '  in  F?    i°?   T?    ^^  &c- 


106  TABLES. 


LESSON  X. 

MEASURE   or   TIME. 

The  natural  units  of  time  are  days  and  years.  These 
are  further  divided  and  arranged  thus : — 

60  seconds  (sec.)  .  make  1  minute  (min.) 

60  minutes  "  1  hour      (hr.) 

24  hours  "  1  day        (da.) 

7  days  "  1  week     (wk.) 

12  calendar  months  "  1  year      (yr.) 

365  days  (or  52  wk.  1  day)       "  1  common  year. 

366  days  (or  52  wk.  2  days)  "  1  leap  year. 
365  da.  5  hr.  48  min.  49j'^^  sec.  "  1  solar  year. 
100  years                                      "  1  century. 

The  Earth  turns  from  west  to  east  one  complete  revo- 
hition  in  24  hours,  thus  making  one  day. 

The  Earth  moves  around  the  Sun  one  complete  circuit 
in  365  da.  5  hr.  48  min.  49 ^"^^  sec,  thus  making  a  year. 

Calendar  months  are  those  months  which  are  called  by 
distinct  names  in  a  calendar.  They  are  twelve,  and  their 
names  are  January,  February,  March,  April,  May,  June, 
July,  August,  September,  October,  November,  December. 

1.  How  many  seconds  in  2  min.?  3  min.?  4  min.?  &c. 

2.  How  many  minutes  in  2  hr.  ?  3  hr.  ?  4  hr.  ?  &c. 

3.  How  many  hours  in  2  days?  3  days?  4  days?  &c. 

4.  How  many  days  in  2  wk.  ?  3  wk.  ?  4  wk.  ?  &c. 

5.  How  many  months  in  2  yr.  ?  3  yr.  ?  4  yr.  ?  &c. 

6.  How  many  days  in  2  yr.  ?  3  yr.  ?  4  yr.  ?  &c. 

7.  How  many  days  in  leap-year? 

8.  How  many  years  in  2  centuries?  3  centuries?  &c.       | 

9.  How  many  seconds  in  ^  min.?  i  min.?  f  min.?  &c.   | 

10.  How  many  minutes  in  ^  hr.  ?  \  hr.?  f  hr.  ?  &c. 

11.  How  many  hours  in  I  day?  \  day?  f  day?  &c. 


TABLES.  107 


LESSON    XL 


CALENDAR  DAYS  AND  MONTHS. 


The  days  of  the  week  are 

Sunday,  or  1st  day. 


Thursday,  or  5th  day. 
Friday,  or  6th  day. 
Saturday,  or  7th  diy. 


February, 
March, 

or 
or 

April, 

May, 

June, 

or 
or 
or 

July, 

August, 

September 

or 

or 

,or 

Monday,  or  2d  day. 
Tuesday,  or  3d  day. 
Wednesday,  or  4th  day. 

The  calendar  months  have  days  as  follows  : — 
January,     or    1st  month,  has  81  days. 

2d   month,  has  28  days ;  in  leap-year  29. 

8d    month,  has  31  days. 

4th  month,  has  30  days. 

5th  month,  has  31  days. 

6th  month,  has  30  days. 

7th  month,  has  31  days. 

8th  month,  has  31  days. 

9th  month,  has  30  days. 
October,  or  10th  month,  has  31  days. 
November,  or  11th  month,  has  30  days. 
December,  or  12th  month,  has  31  days. 

Commit  to  memory  the  following  lines  : — 
Thirty  days  have  September, 
April,  June,  and  November : 
And  all  the  rest  have  thirty-one. 
Save  February,  which  alone 
Has  twenty-eight;  and  we  assign 
To  this,  in  leap-year,  twenty-nine. 

Or, 
The  ff^'irth,  eleventh,  ninth,  and  sixth, 
H'lve  thirty  days  to  each  affixed : 
And  all  the  rest  have  thirty-one, 
Except  the  second  month  alone, 
To  which  we  twenty-eight  assign, 
Till  leap-year  gives  it  twenty-nine. 


g 

« 

108 

TABLES. 

LESSON 

XIL 

MISCELLANEOUS 

TABLES. 

1. 

Of  collections  of  things. 

12  things 

make  1  dozen.                 | 

12  dozen, 

or  144  things. 

i( 

1  gross. 

12  gross, 

or  1728  things^ 

a 

1  great  gross. 

20  things 

a 

1  score. 

2.  Of  Paper. 

24  sheets 

make  1  quire.                    | 

20  quires. 

or  480  sheets. 

a 

1  ream. 

2  reams 

(( 

1  bundle. 

5  bundles,  or  10  reams. 

u 

1  bale. 

3.  Of  Books. 

A  folio  (fol.) 

is  made  of  sheets  folded  in  2  leaves.         1 

A  quarto  (4to) 

- 

-      4       " 

An  octavo  (8 

vo) 

- 

-      8       " 

A  duodecimo 

(12mo) 

- 

.     12       « 

An  18mo 

- 

- 

-    18      " 

A  24mo 

- 

- 

-    24      " 

A36mo 

- 

- 

-     36       " 

1.  How  many  things  in  2  dozen?  3  dozen?  &c. 

2.  How  many  things  in  2  gross  ?    3  gross  ?  &c 

3.  How  many  things  in  2  score?    3  score?  &c. 

4.  How  many  sheets  in  2  quires  ?  3  quires  ?  &c. 

5.  How  many  quires  in  2  reams?  3  reams?  &c. 

6.  How  many  sheets  in  2  reams  ?  3  reams  ?  &c. 


THE   END. 


^ 


OSGOOD'S 

PROGRESSIVE  SERIES. 


Osgood's  Primary  Lessons,  comprising  fourteen  cards 

on  seven  boards. 
Osgood's    Progressive    Primer,   36    pages,   12mo, 

with  illustrations. 
Osgood's  Progressive  Speller,  for  common  schools. 
Osgood's  Progressive   First  Reader,  for  primarj 

classes  in  common  schools. 
Osgood's    Progressive    Second    Reader,    conwii 

ing    simple    lessons    in    reading    and    spelling,   far 

primarj  and  medium  classes. 
Osgood's   Progressive   Third   Reader,    containing 

lessons   in    reading  and   spelling,    together  with   the 

primary  rules  for  reading,  suitable  for  medium  classes. 
Osgood's    Progressive    Fourth    Reader,  designed 

for   grammar   schools,   containing   extracts   from  our 

best    authors,    in   prose    and    poetry,    together  with 

prominent   principles   and    general  rules  for  reading, 

and  their  application. 

Osgood's  Progressive  Fifth  Reader,  designed 
for  the  highest  classes  in  schools  and  academies, 
and  containing  a  complete  system  of  elocutionary 
and  rhetorical  rules,  with  choice  and  elegant  selec- 
tions from  the  best  American  and  English  authors. 

Dean's  Primary  Arithmetic,  for  primary  classes  in 
public  schools. 

Dean's  Public  School  Arithmetic,  for  public  s< 

and  academies. 
Burtt's  Elements  op  English  Grammar,  8ju 

and  Analytic,  for  the  use  of  school*?,  academies] 

private  learners. 


